Download Stats Class Notes

Stats Class Notes
8/31
Definitions of Statistics:
1. Statistics consists of facts and figures.
Fact: A significant number of ppl in the U.S. Do not have health insurance.
Figure: Four million A/ns do not have health insurance.
Examples of statistics: average income, crime rate, birth rate, average snowfall, etc.
2. Statistics refers to a set of mathematical procedures for collecting, organizing, summarizing, and interpreting
information.
Ideally, we would like to obtain information from: Populations: the set of all the individuals of interest in a particular study.
Example: All children of divorced families in the U.S., or all responses from men and women in the U.S., etc.
However, we mostly examine samples: the set of individuals selected from a population, usually intended to represent the
population in a research study.
- achieved by random sample of children from divorced families, random sample of men and women.
1) sampling with replacement: in order to maintain equal probability of being selected, individuals are selected and placed
back into the pool. This maintains an equal chance for each subject.
Constraints on samples: time and money!!!
Parameter: is a value, usually a numerical value that describes a population. It can come from a single measurement, or ti can
come from a set of measurements from the population.
Statistic: is a value, usually a numeric value that describes a sample. It can come from a single measurement or a set of
measurments from the sample.
Relationship b/w a population and a sample:
We draw inferences from our sample to the wider population. (read inferential statistics)
The two branches of stats:
Descriptive Stats: refers to statistical procedures used to summarize, organize, and simplify data such as the mean, standard
deviation, the range, etc. Presented by tables and graphs.
Inferential Stats: Consist of techniques that allow us to study samples. The results from the samples can then be gernalized to the
wider population. **A sample provides only limited information about the populations.**
Sampling error: is the discrepancy, or amount of error, that exists between a sample statistic and the corresponding
population parameter.
The difference between constants and variables.
Methods:
Correlational method
Experimental method:
- the goal: to establish a cause and effect relationsihp. 1 variable manipulated by researcher (I.V.) and 2nd is observed by
researcher (D.V.)
- Question: Does the I.V. Cause a change in the dv?
~ extraneous variables that oculd affect the D.V. Are controlled for by the reseacher. Example: average I.Q.,
age, time of day, etc. (usually fall under either participant variables and environmental variables)
Non-experimental studies:
- there is no manipulation or control over group assignment in order to create equivalent groups.
- can be age, gender, etc. Then compare the different groups.
Variables and Measurement:
Constructs:
Operational definition:
Random Variables:
Types of Variables:
1) numeric discreet: whole numbers, counting, indivisible categories.
2) numeric continuous: is divisible into an infiinite number of fractional parts; contained within an interval, lower real
limits, upper real limits. E.g., IQ of 100 is between 99.5 and 100.5.
3) categorical and qualitative variables: represented by categories; must be mutally exclusive; must be exhaustive
Measurement: involved translating empirical relatinships b/w objects into numberical relationships.
scales of measurement:
-- Nominal Scale: labels observations into categories gives us qualitative differences, notquantitative differences.
Example: gender, race, religion, etc.
-- Ordinal Scale: categories have separate names; ordered from low to high or high to low, gives us direction of the
difference. Example: social class (upper, middle, lower), Likert type responses. We do not know the magnitude of the difference
between categories.
-- Interval Scale: categories are ordered, intervals are the same size; scale has no absolute zero that indicates the
"absence of" it provides information about the magnitude of the difference between 2 measures. Example: intelligence,
temperature, attitudes, etc.
-- ratio scale: equal intervals; meaningful zero which indicates the "absence of"; all mathematical operations are possible.
Constructing a Grouped Frequency Distribution:
1) sort data from low to high
2) H - L + 1 to determine the number of rows
3) using width of 5, interval / width = 9.4 intervals; round up to 10 intervals
4) bottom score of each interval must be a multiple of the width; lowest score is 41, begin with 40. WIDTH= the range of scores in
each interval.
Percentiles, percentile ranks, and Interpolation:
- understand how to set up frequency table and construct cumulative frequency and cumulative percentages.
9/7
**when constructing histograms, need to include all intervals.**
Measures of Central Tendency:
The most common method:
1) for summarizing and
2) describing a set of scores, observations, or measurements.
Other terms for Measures of Central Tendency are:
1) the average / arithmetic average
2) typical score
3) a single value that best represents a data set
Purpose of Central Tendency:
1) to provide a single description of the entire population or sample
2) to allow us to compare groups of individuals, scores, measurements.
**One single measure of central tendency does not fit ALL distributions.**
1) Mean: considers each value in the data set
2) Median: divides the distribution in half
3) Mode: value that occurs most often.
When to use which Measure:
Mean: when data are normally distributed, when we have a bell-shaped curve, when most of the values are located around the
middle with fewer values at either end.
- mean is considered the balance point of the distribution of scores. The total distances below the mean = the total
distances above the mean.
- Weighted mean: combining sets of scores to determine the overall mean. = sum of group 1 + sum of group 2 / n 1 + n
2
- or using ratios
- know what happens to mean when: 1) score is added, 2) when a score greater than the mean is removed, 3) adding or
subtracting a constant to each score, 4) when mult or div a constant to each score.
Median:
- know how to calculate when odd #of scores (n + 1)/2=position of median, even #of scores, when several scores tied with the
median:
~~ Median = X(lrl) + (.5N - f(below LRL))/ftied
- used when: there is skew in the frequency distribution
Mode:
- used when: with nomial data
___________
Measures of Variation:
1) Range
2) Interquartile Range and Semi-interquartile range
3) Standard Deviation and Variance - population
4) Standard Deviation and Variance - sample
- 2 concepts that help us in differentiating what is normal and what is extreme or abnormal are: 1) the average and 2) the variance
Variability: describes a distribution in terms of the distance from score to score or the distance from each score to the mean.
When variability is SMALL, there is a greater chance that you will randomly select an average score (or individual)--and vice versa.
-- this is the same when drawing a sample from a population. The more variance in the population, the less likely our
sample is representative of the population.
Range= URLmax - LRLmin
Interquartile range: Q3 - Q1; considers the middle 50% of the distribution. Need to find the 25th percentile and 75th percentile.
Semi-interquartile range: (Q3 - Q1)/2
Standard Deviation: the most common and most important measure of variability.
- the standard or typical distance of scores from the the mean.
-standard deviation = square root of variance.
**Deviations computed from sample means are not "real deviations". Sample variability underestimates the populations variability
and thus results in biased estimates of the population variability.***
- to correct for this bias, we use degrees of freedom: df = n-1
- in general, with a sample of scores, the first n-1 scores are free to vary, but the final score is restricted by the mean.
9/14
Raw score: an untransformed observational measurement
Z-score: a standardized score with a sign that indicates direction from the Mean and a numberical value equal to the distance from
the Mean measured in SD.
Standard score: a score that has been transformed into a standard form.
Standardized distribution: An entired distribution that has been transformed to create predetermined values of mu and theta.
**With a mean and a standard deviation we can describe the entire population.
Z-scores
Two reasons: 1) will give us the exact location of a score (i.e,. The original X value within a distribution
2) by standardizing entire distribution, direct comparisons can be made between distributions even if the units of the
original distributions are different.
Formula: (on written notes)
Probability and its importance to inferential statistics:
Inferential statistics:
What do we mean by inferential stats?
-- Whenever we draw a simple random sample from a population:
a) where each individual has an equal change of being selected and
b) the probability of being selected is constant.
c) we can use the findings from the sample and generalize to the wider population.
-- we cannot generalize the exact result of the sample to the population, therefore we use probability.
Probability: the number of target outcomes / total number of outcomes. Must have a random sample.
Probability and proportion or spoken of equivalent
** Probability is always related to in the long run, or on average.***
% of Z-scores:
Z=1, 34.13%
1<z<2, 13.59%
z>2, 2.28%
Binomial Distributions:
-- (SEE HANDOUT)
9/21
**Seldom have access to the entire population. Take sample from population, then generalize to the populatioon.***
Inferential Statistics is based on the sampling distribution of the means.
**The difference between the sample mean and the population parameter is called sampling error.***
-- larger samples sizes more closely approximate the population, therefore, larger samples are better, more representative of the
actual mean.
-- however, samples randomly drawn from the population provide an incomplete picture of the population.
We can predict sample characteristics when they are based on the distribution of sample means.
Distribution of sample means: is the collection of sample means for all the possible random samples of a particular size (n) that
can be obtained from a population.
-- the distribution contains sample means, not individual scores.
Central Limit Theorm:
- For any population (irrespective of shape, mean, or standard deviation) with mean mu and standard deviation sigma, the
distribution of sample means for sample size n will have a mean of mu and a standard deviation of sigma/sqrt(n) and will approach
a normal distribution as n approaches infinity (when the sample size n>30, the dsitribution of sample means will closely
approximate a normal distrubution).
Law of large numbers: the larger the sample size, the more probably it is that the sample mean will be close to the population
mean.
Standard Error: It measures the standard amount of difference between the mean of the distribution of means and the population
mean.
Biased vs. Unbiased Stats:
- mean of all sample means = population mean and is therefore unbiased.
- the average of all sample variances is also equal to the population variance and, therefore, is condsidered an unbiased estimate of
the population variance.
**The sample variance is unbiased, but the SAMPLE STANDARD DEVIATION is biased. The average of the square roots is not equal
to the square root of the average.**
10/5
Central Limit Theorem:
- the distribution of sample means (of all possible samples of a given size)
- Mean will = pop mean
- standard deviation = pop SD / sqrt(n)
-- note that the larger the sample becomes, the closer it's mean will be to the population mean.
[MAKE SURE YOU KNOW AND CAN REPLICATE THIS IN YOUR OWN WORDS!!!]
Ch 8: Hypothesis Testing
Hypothesis Testing uses z-scores when popSD is known and t-scores when popSD is not known.
In addition, we must make the following assumptions:
A. random sampling: sampels must be representative of the population from which theyhave been drawn
B. Indepdendent observations: section of the first event (subject) doe snot effect the selection of the second event.
C. The value of popSD is unchanged: we assume that the popSD for the unknown population after the treatment has been
administered, popSD is the same as it was before treatment.
D. Normal sampling distribution: to evaluate hypothesis with z-scores, we use the unit normal table to tidentifythe critical
region; we can use the table onlyif the distribution of means is normal.
Hypothesis: a theory, a belief, a claim, or an asswertion which the Researcher makes about the population parameter when the
population mean is unknown.
Hypothesis testing is used for making decisions about specific values of population parameters.
-- always remember that your hyposthesis is either confirmed or disconfirmed... There is no proving in stats
Caution: our rejection of the null hypothesis is based on evidence from the sample that alternative hypothesis is more likely to be
the case. -- if we fail to reject the null hypothesis, we can only condlue that there is sufficient evidence to warrant acceptance of
the null hypothesis.
--- can only speak in terms of sufficient evidence
- we state our null hypothesis in terms of the population parameter even though our data is obtained from a sample b/c we are
interested in making inferences about the population--generalizng to the population.
The Null Hypothesis is the one that is ALWAYS tested.
- The null hypothesis always refers to a specified value of the population parameter mu not a sample statistic.
- The Null hypothesis always contains an =
- The alternative hypothesis never contains an =
---- we must differentiate between directional and non-directional tests.
** when writing hypotheses, must write both the null and alternative.
Set Decision Criteria:
***Remember: hypothesis testing is based on the sampling distribution of the means. With this in mind, the critical region consists
of sample outcomes that are very unlikely if the null hypothesis is correct.
Alpha Level / Level of significance
1. Alpha is determined by the researcher BEFORE data is collected.
2. Alpha is ud to obtain a CRITICAL VALUE for the test statistic (i.e., how big the result much be before the researcher can claim a
particular result)
Two types of errors:
Type I error: incorrectly rejecting a true null-hypothesis. Stating that a treatment had an effect when it actually had no effect. Can
occur with extreme or misleading samples.
-- a more serious error b/c it leads to false reports.
Type II error: incorrectly failing to reject a false null hypothesis. Stating that a treatment has no effect when it actually does have
an effect. This can occur when a treatment has a very small effect.
**In selecting the alpha level, the primary concern is reducting Type I error. To reduce risk of Type I error, can reduce alpha; by
using smaller alpha level, we are more confident that our treatment had an actual effect.
Effect Size:
Because a hypothesis test evaluate the relative size of a treatment effect, not the absolute size; it is helpful to calculate an effect
size once the null hypothesis has been rejected.
Cohen's d: mean difference / standard dev
Power of a test: the probability that the test will correctly detect a real treatment effect.
- Power = P(rejecting a false H0) = 1 - Beta
- influenced by:
- increasing alpha
- changingfrom a 2-tailed to 1-tailed
- SOMETHING ELSE
[MISSING CLASS NOTES UP TO BELOW DATE]
10/19
The three distributions:
1. Population distribution
2. The standardized distribution (z)
3. Sampling distribution of the means.
T-testfor Two Related Samples
- The repeated measures design:
-- related subjects or
-- within subjects design
- is preferred to an indepdendent measure studywhen the R wants to observe CHANGES in behavior in the SAME SUBJECTS, as in
learning, developmental or other changes over time.
- The sample of difference scores are used to answer questions about the general population.
Consists of:
1. 1 subject sample (a single group of individuals)
2. 2 statistical samples
Scores in each condition must be NUMERICAL values that allow calculation of the sample mand and sample variance
Difference scores: score 2 - score 1
T measures:
- the numerator measure the difference b/w MD and the hypothesized popMD
- denominator measures the standard difference that is expected by chance
Effect size: MD / SD
R2 = is the same as before
Advantages of the related samples t-test:
1. A repeated-measures design requires fewer subjects.
2. A repeated-measures design is well suited to study learning, development, and other changes that take place over time.
3. Individual differences are eliminated (from time 1 to time 2); variance is reduced: the chances of finding a significant result is
increased.
Disadvantages of design:
1. Carryover effect: a subject's response in the second treatment is altered by lingering afteraffects from the first treatment.
Carryover effects are related directly to the first treament.
2. Progressive error: Subject's performance either declines (fatigue) or increases over time (practice effect). Progressive error
occurs as a function of time, indepdendent of which treatment condition is presented first or second
- Solution: counterbalance the order of presentation of treaments: systematically varying the order of conditions for participants in a
within-subjects experiment.
Assumptions of the related samples t-test:
1. Observations within each treatment condition must be independent. Inside each treatment, the scores are obtained from
different individuals and should be independenof one another.
2. The population distribution of difference scores (D values) must be norm. We are safe with samples of size n > 30.
10/26
The purpose of estimation:
- is to tdetermine how much of an effect a treatment has. It is to use sample data that provide values that approximate population
parameters.
Similarities:
- Both procedures are inferential techniques
- Both use sample data to find unknown population parameters.
- Both use the same t-statistic equation
- Both use the t-distribution
Differences:
- A hypothesis test determines IF there was a treatment effect
- An estimate determines a number of values of the treatment effect.
When used?
- After a hypothesis has been rejected.
- When we know that there is an effect and we want know the magnitude of the effect.
- When we want some basic information about an unknown population mean.
KNOW: difference b/w statistical and clinical significance
- the mangitude of the statistical significance may not be big enoug to make it of any practical value.
Two types of estimates:
- Point Estimate: a single score extimate
- uses a single value as an estimation of the unknown population parameter.
- very precise, but very little confidence in that value
- Interval Estimate: a range of scores
- when an interval estimate is accompanied by a level of confidence, it is called a "confidence interval"
In estimation, we begin by estimating where the sample is located in the T-DISTRIBUTION. We estimate WHAT the T-VALUE ought
to be.
We select a "reasonable" value for t.
- A t-value close to the center of the distribution relates to a high-probability outcome (t=0).
- for point estimate, my sample mean is always the estimated population parameter (b/c t=0)
***The larger the sample size, the narrower the confidence interval!!!*****
-- if we calculate a 95% a confidence interval, then, out of all the possible different confidence intervals we could calculate, 95% of
them will contain the population mean.
Parametric Tests:
- t, z; tests specific population parameters
Assumptions:
- Samples are randomly drawn
- observations are independent
- variables are normally distributed
- variables are ratio or interval
Non-Parametric Tests:
(e.g., Chi-Square tests)
- are intended for research questions concerning the proportion of the population in different categories.
Data consists of frequencies: participants are classified into categories (there are no numberical scores for each individual).
Sample mean and variance are NOT computed.
Frequency observed: is the number of individuals in a particular category for our sample.
Hypothesis testing:
Ho: in the general population, there is no relationship between the 2 variables (they are independent)
H1: There is a consitsten, predictable relationship between the 2 variables (they are not indepdent)
Or
H0: In the general population, the distribution....
H1: ....
Df: (rows - 1)(columns - 1)
Assumptions and restrictions:
1. Independence of Observations. Each observed frequency reflects a different individual
2. Expected frequency of each cell must be 5 or more.
Effect size for Chi-square:
- When 2 x 2: Phi-coefficient
- When larger than 2 x 2: Cramer's V
11/2
One-Way ANOVA:
- Analysis of Variance (ANOVA) is a statistical technique used to test mean differences among 2 or more treatments or populations.
- is an inferential procedure; we use sample data as the basisfor drawing conclusinos about populations
- ANOVA: has procedures available for both independent or repeat measures
Because we cannot compare more than 2 means directly, we compare means through an analysis of variation in the data both
among and withing the groups.
*consists of one IV and one DV*
-- the independent measures analysis of variance analyses the total variability into two components:
Total Variability:
1. Between-treatment variance:
-- measures the differences due to treatment effect.
2. Within treatments variance: measures differences due to chance alone.
F-statistic (F-ratio): variance between sample means vs. variance expected by chance.
**We are looking for mean differences, but we are doing that by looking at variances.**
** See formulae on supplemental notes.**
If F-ratio = 1; there is no treatment effect, groups do NOT differ.
Repeated Measures ANOVA:
- for a single sample, and the same set of individuals; scores are obtained for the different treatment conditions.
-- can also be used w/ NON-experimental studies.
e.g., measurements of depression scores before therapy, after therapy, and 6 months after therapy.
* IV is not manipulated by R *
used to: determined if there are differences b/w 3 or 4 conditions or if there si a change in scores over time.
Advantages:
- individual differences do not contribute to the analysis.
- individual differences are automatically removed from the b/w treatments SSb in the numberator of the F-ratio (because the same
set of subjects is used)
BUT:
- experiment-wise or unsystematic differences sill exist. Such differences are unexplained and are considered due to chance.
11/16
The two-factor analysis of variance: designates a single DV and uses two IVs (always categorical) to determine how the IVs
influence the DV.
The structure of a 2-factor study can be presented in a matrix.
2 x 2 Factorial Factorial design: 2 factors, each with 2 levels.
2 x 3 Factorial design: 2 factors, 1 with 2 levels, 1 with 3 levels.
-- Most of the time, the factor with the most levels will be the "B" factor.
Goal: to evaluate the mean difference that may be procduec by :
1. either of these tow factors independently or by the
2. two factors acting together.
A 2 x 3 independent research design produces 6 separate treatment conditions = six separate samples.
Three Separate Hypotheses make up a 2-factor anova.
-- Main Factor A:
1. muA1 = muA2
-- Main Factor B:
2. muB1 = muB2 = muB3
-- Interaction Effect
3. There is no interaction between factors A and B. All the mean differences between treatment conditions are explained by the
main effects of the 2 factors.
Interction Effects:
- when the effects of one variable depend on another factor.
- when main effects cannot be explained by looking at the individual cells, we have an interaction.
- when we have an interaction, we really look at interpreting that interaction.
Assumptions:
1. Obersvations within each sample must be independent.
2. Normal populations
3. Homogeneity of variance.
11/30
Correlation
- an inferential procedure.
- only measures an association NOT A CAUSATION
-
data are OBSERVED, not manipulated. Only observing what is happening in the environment.
2 sets of data for each individual
Variables are continuous, measured at the interval/ratio scales
Correlation is bivariate.
The Pearson Correlation:
3 Characteristics:
1. Direction: positive or negative
2. Form: measures a linear relationship.
3. Degree: the magnitidue the relationship to which the data fits the form
-- useful to use a scatter diagram to analyze the relationship b/w two variables.
r-squared = the coefficient of determination: how much of the variance in one variable is accounted for by the variance in the other
variable.
*A correlation does not explain why one variable is related to the other. it only tells us that the two variables are associated to the
other.*
To attribute cause, 3 conditions are necessary:
1. X must precede Y
2. X and Y must covary
3. No rival explanations can account for the covariance of X and Y.
Causal Relationships: If we have a true experiment with a quantitative, I.V. that is manipulated we can make causal statements.
BUT the ability to make a causal statement comes from executing a true experiment, not calculating the Pearson r.
Know that there may be a correlation, but it may not be linear.
To measure non-linear correlations, use SPEARMAN.
Does a correlation exist in the population??
- H0: rho = 0
- H1: rho ~= 0
Important: Limitations
1. Only describes relationshp, not why related
2. Can be greatly affected by restricted range!!
3. Correlation is not a proportion. Not tell you how accurately you can predict.
4. Can be greatly affected by outliers.
KNOW WHERE AND WHY CORRELATIONS ARE USED: p. 510 in text.
Simple Linear Regression:
When there is a consistent relationshp between 2 variables, we can use 1 variable to predict the outcome of another variable.
X - variables are the predictor variables
Y - variables are outcome variables
Simple linear regression or least squares model is used for prediction.
Goal: to find the best fitting straightline between X and Y; the line that minimizes the differences between the observed values of Y
and the predicted values of Y.
Regression Line: Identifies the center or central tendency of the relatinship in the same way as the mean defines the center of a set
of scores.
In order to make any predictions, WE MUST HAVE ALL POSSIBLE VALUE-- aka, cannot have restricted range.
Y = bx + a
- a and b are constants
- a is the Y-intercept; where the regression line intercepts the Y-axis; aka, the value of Y when X is zero.
- b is the slope; tells us how much Y changes when X increases by 1 unit (point). aka the change in vertical distance for a given
change in the horizontal distance.
For every X value in the data set, the linear equation will deterimine a Y value on the regression line. This value is the predicted
value of Y.
The regression line is used to generate predicted y value for any known value of X.
The relationship b/w X and Y must be LINEAR or well approximated by a straight line. If not, other methods must be used.
12/7
Multiple Regression:
The multiple regression equation or population model is an extentio of the bivariate regression model:
Error: is because predictions are not perfect; the residual (how far off are predictions are on average).
Assumptions:
1. The IV and the DV have a linear relationship
2. All populations are normally distributed.
2. The DV is continuous and is measured on (at least) and interval scale.
3. The regression model errors are normally distributed.
4. The mean of the errors is 0
5. The errors have a constant variance
- should be within 2 standard deviations of the standard error
6. The error terms are independent
7. successive observations of the D.V. are uncorrelated -- not responsible
GOAL: to estimate the effect of several I.V.s on a D.V.
ADVISABLE: to construct scatterplots for each I.V. with the D.V. to establish linearity.
Know difference between population model and sample model.
Multiple regression is really a regression plane, not just a straight line.
- Each regression coefficient represents a different slope.
- The slopes are referred to as PARTIAL SLOPE COEFFICIENTS or PARTIAL REGRESSION COEFFICIENTS.
Variables that can be used:
1. quantitative
2. Qualitative (referred to as dummy variables coded 0 or 1, 1 or 2, etc.)
Remember, in MR, population parameters are estimated from SAMPLE DATA.
The multiple regression equation estimates the best fitting plane to the data. It minimizes the errors of prediction.
a = the predicted value of Y when ALL I.V.s are zero.
Interpretation of Partial Coefficients:
b1: is the partial regression coefficient; is the coefficient for the rgression of Y when we partial out the whole constant and the
effects of other variables.
b2: is the partial slope of the linear relationship between the 2nd IV and the DV, etc. holding constant the other variables.
-- so, each coefficient refers to how much change occurs in the DV for a one-unit change in the IV given that all of the other values
are held constant.
**In the selection of the I.V., it is best to include variables that are:
1. strongly related to the D.V.
2. but are uncorrelated or weakly correlated with each other.
- when two IVs are correlated .7 or greater, it is best to throw out one of the variables.
**How big should the sample be in MR?
-- AT LEAST 4X THE NUMBER OF IVs
SPSS provides the Collinearity Diagnostics and gives us a Variance Inflation Factor for each I.V. If VIF is > 5, delete the
variables with the largest VIF values.
We can also examine Tolerance in SPSS. Tolerance values range from 0 to 1. A value of 1 indicates that an IV has little of its
variability explained by the other IVs (this is good). A value of 0 indicates that a variable is almost a linear combination of the other
IV (such data are called multi-collinear).
Multiple Coefficient of Determination = R-square. (as opposed to r-square for SLR)
R-square is the proportion of the variation in the D.V. that is explained by the DV's relationship to all IVs in the model.
e.g., 80.4% in heating cost is explained by the linear relationship of the 3 IVs in the regression model.
*When examining a multiple Regression model, we must examine:
1. Is the overall model significant?
-- look at ANOVA table
-- testing the Betas; are their values significantly different from 0?
-- H0: B1 = B2 = B3 = 0
-- H1: At least one B is not = 0
-- If the F-calculated is significant, then themodel is a better predictor than the average of Y.
2. Are the individual variables significant?
-- look at the predictor significance
-- if a predictor is not significant, then remove it as a predictor.
3. Is the standard error too large to provide meaningful results?
--- compare standard error (the standard errors of prediction) to standard deviation of Y.
4. Have the regression assumptions been met?
*A regression model is based on sample data and is subject to sample error
****From sample betas, you cannot say which is the greatest predictor. You must look at the STANDARDIZED BETAS.***
Interpretation of Coefficients:
e.g., : B=-4.95: For each additional increase in the mean outside tempurature, we expect heating costs to decrease by $4.95 per
month for houses with the same insulation and the same aged furnace. (holding other variables constant)
-- when making comparisons between 2 different scenarios and predicting values, hold other non-changing variables by making
them 0.
**If the overal model is significant, this means that at least 1 of the IVs explains a significant proportion of the variation in Y.
FINAL EXAM:
A. KNOW ASSUMPTIONS for each test
B. When you are seeing an interaction, basically forget about the main effects; statistically there are main effects, but the
interpretation should focus on the interaction effect.
C. For two-factor analysis; helpful to put means in the cells; and to identify levels of independent variables.