S1 Past Paper Booklet - The Grange School Blogs
... travelled 19 000 miles in 2005. State, with a reason, but without further calculation, whether the value of Spearman’s rank correlation coefficient will increase, decrease or stay the same. ...
... travelled 19 000 miles in 2005. State, with a reason, but without further calculation, whether the value of Spearman’s rank correlation coefficient will increase, decrease or stay the same. ...
Advanced Math Functions Blackline Masters
... 3. Is this particular tax structure fair? Why or why not? Answers will vary, but students should identify this tax structure as being progressive since the tax increases as the income increases. Blackline Masters, Advanced Math – Functions and Statistics Louisiana Comprehensive Curriculum, Revised 2 ...
... 3. Is this particular tax structure fair? Why or why not? Answers will vary, but students should identify this tax structure as being progressive since the tax increases as the income increases. Blackline Masters, Advanced Math – Functions and Statistics Louisiana Comprehensive Curriculum, Revised 2 ...
Lecture IX -- SupervisedMachineLearning
... Unlikely that every occurrence of “minute” is 100% spam Unlikely that every occurrence of “seriously” is 100% ham What about all the words that don’t occur in the training set at all? 0/0? In general, we can’t go around giving unseen events zero probability ...
... Unlikely that every occurrence of “minute” is 100% spam Unlikely that every occurrence of “seriously” is 100% ham What about all the words that don’t occur in the training set at all? 0/0? In general, we can’t go around giving unseen events zero probability ...
Linear Least Squares Problems
... of minimizing the sum of the absolute residuals with the added condition that they sum to zero. He showed that the solution must then satisfy exactly n out of the m equations. Gauss argued that since greater or smaller errors are equally possible in all equations, a solution that satisfies precisely ...
... of minimizing the sum of the absolute residuals with the added condition that they sum to zero. He showed that the solution must then satisfy exactly n out of the m equations. Gauss argued that since greater or smaller errors are equally possible in all equations, a solution that satisfies precisely ...
The Correlation between U.S. Tornadoes and Pacific Sea Surface
... are considered when the correlation between SST and tornadic activity is examined. Given the effect of El Niño and La Niña on the position of the jet stream, it is conceivable that SST can have a different effect on tornadic activity depending on the particular geographic region wherein the tornad ...
... are considered when the correlation between SST and tornadic activity is examined. Given the effect of El Niño and La Niña on the position of the jet stream, it is conceivable that SST can have a different effect on tornadic activity depending on the particular geographic region wherein the tornad ...
The Gender Pay Gap in Europe
... Relating to the e↵ect family life has on female wages is the e↵ect of childbirth. In the past, starting a family would often lead to the mother leaving employment for a significant time period or even leaving the workforce alltogether. In recent times this is not observed as much, and the e↵ect of c ...
... Relating to the e↵ect family life has on female wages is the e↵ect of childbirth. In the past, starting a family would often lead to the mother leaving employment for a significant time period or even leaving the workforce alltogether. In recent times this is not observed as much, and the e↵ect of c ...
PLS: Caveat Emptor On the Adoption of Partial Least Squares in
... The second question has attracted much less attention in the literature. A key problem here is that although PLS weights are often referred to as being “optimal”, the literature is not clear for which specific purpose the weights are optimal. Some authors argue that the weights are optimal for maxim ...
... The second question has attracted much less attention in the literature. A key problem here is that although PLS weights are often referred to as being “optimal”, the literature is not clear for which specific purpose the weights are optimal. Some authors argue that the weights are optimal for maxim ...
X-bar Charts
... shifts in the process. For example, there might be a positive trend in the last ten subgroups, but until a mean goes above the upper control limit, the chart gives no indication that a change has taken place in the process. Runs tests can be used to check control charts for unnatural patterns that a ...
... shifts in the process. For example, there might be a positive trend in the last ten subgroups, but until a mean goes above the upper control limit, the chart gives no indication that a change has taken place in the process. Runs tests can be used to check control charts for unnatural patterns that a ...
Cumulative Sum (CUSUM) Charts
... customizable. The data for the subgroups can be in a single column or in multiple columns. This procedure permits the defining of stages. The target value and sigma may be estimated from the data (or a subset of the data), or a target value and sigma may be entered directly. The CUSUM chart may be u ...
... customizable. The data for the subgroups can be in a single column or in multiple columns. This procedure permits the defining of stages. The target value and sigma may be estimated from the data (or a subset of the data), or a target value and sigma may be entered directly. The CUSUM chart may be u ...
2416grading2415 - Emerson Statistics
... statistically significant with a significance level of 0.05 (P<0.001). The increase will not be unusual if the true average increase amount falls within the interval of 34.5773mg/dl to 39.0890 mg/dl as log transformed crp level goes up per unit. We can with high confidence reject the null hypothesis ...
... statistically significant with a significance level of 0.05 (P<0.001). The increase will not be unusual if the true average increase amount falls within the interval of 34.5773mg/dl to 39.0890 mg/dl as log transformed crp level goes up per unit. We can with high confidence reject the null hypothesis ...
Statistical Methods (201112)
... partial non-response) and to missing values that should have been present. Reasons for answers not being provided are that the respondents are not willing or able to answer a question. For example, people are sometimes not able to answer a question that is complicated or difficult to understand, and ...
... partial non-response) and to missing values that should have been present. Reasons for answers not being provided are that the respondents are not willing or able to answer a question. For example, people are sometimes not able to answer a question that is complicated or difficult to understand, and ...
Long-Run Covariability
... simplification offered by these averages is that they are normally distributed in large samples even though the stochastic process generating the data may exhibit substantial persistence (Müller and Watson (forthcoming)). This allows large-sample inference about covariability parameters to be transfo ...
... simplification offered by these averages is that they are normally distributed in large samples even though the stochastic process generating the data may exhibit substantial persistence (Müller and Watson (forthcoming)). This allows large-sample inference about covariability parameters to be transfo ...
Linear regression
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y. Given a variable y and a number of variables X1, ..., Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ""lack of fit"" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ""least squares"" and ""linear model"" are closely linked, they are not synonymous.