Download Regression and Forecasting Models

Assignment 2
IOMS Department
Regression and Forecasting Models
Professor William Greene
Phone: 212.998.0876
Office: KMC 7-90
Home page:
people.stern.nyu.edu/wgreene
Email:
[email protected]
Course web page:
people.stern.nyu.edu/wgreene/regression/outline.htm
Assignment 2
Notes:
(1) The data sets for this homework (and for the other problem sets for this course) are
all stored on the home page for this course. You can find links to all of them on the
course outline, at the bottom with the links to the problem sets themselves.
1. Problem 10.56(c), Text, page 596.
x and y are uncorrelated. The correlation is 0.0 as is the square
Welcome to Minitab, press F1 for help.
Descriptive Statistics: x, y
Variable
x
y
N
7
7
N*
0
0
Mean
2.571
2.000
SE Mean
0.369
0.309
StDev
0.976
0.816
Minimum
1.000
1.000
Q1
2.000
1.000
Median
3.000
2.000
Q3
3.000
3.000
Maximum
4.000
3.000
Correlations: x, y
Pearson correlation of x and y = 0.000
P-Value = 1.000
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Assignment 2
2. Problem 10.57, Text, page 597
a. Y = β0 + β1X + ε
b. correlation of 0.68 is moderately high. R2 in the regression would be a bit less than
.5.
c. If the correlation is positive the slope of the regression is also positive.
d. If the true correlation were actually zero, there is only a .001 probability that the
observed value could be as high as .68. .68 would be very unlikely.
e. R2 = .4624. This would be the R2 if y were regressed on x.
3. The class discussion about the Monet paintings model was based on the 328 signed
paintings in the data base. For this exercise, you will reproduce the model using all 430
sales, rather than just the signed ones. This exercise uses the Monet.mpj data file.
a. Produce a scatter plot with the log of the area on the horizontal axis and the log of the
sale price on the vertical. What does the figure suggest about the regression?
The figure suggests that the log price and log surface area are positively
correlated.
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Assignment 2
b. Compute the regression of log(price) on log(area) and report all results. What is the
value of R2 for your regression? Using the F statistic, determine whether there appears
to be a significant relationship between log(area) and log(price).
R2 = .334. The F statistic of 214.25 is far more than 4.0. We reject the hypothesis
of no relationship. The t statistic of 14.64 (far more than 2.0) implies the same
conclusion.
c. Form a confidence interval for the coefficient β1 for your model.
1.32609 ± 1.96(.09060)
4. Referring to the results you obtained in part 3, the painting IRIS sold for $2.262M.
The painting is 47.2 inches high and 39.4 inches wide. Use your model to predict how
much this painting would sell for. Note, your model predicts the log of the sale price, so
once you predict the log of the sale price (and the lower and upper confidence limits),
compute exp(prediction) to predict the price, and likewise for the upper and lower
confidence limits.
log(47.2 x 39.4) = 7.52816
using descriptive statistics, log average area = 6.6801
Prediction = 5.2899 + 1.32608(7.52816) = 15.23219.
Forecast standard error = sqr[1.103542(1 + 1/430) + (7.52816 – 6.6801)2 .090602]
= sqr (1.226536) = 1.10749
Interval = 15.23219 ± 1.96(1.10749) = 13.0651 to 18.29968.
In dollars, the prediction is 4,123,405 and the interval is
472,172.69 to
97,921,823.61
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Assignment 2
5. Are more educated people happier people? The data set happiness.mpj contains the
Forbes Magazine data on happiness, by country. The two variables of interest in this
exercise are HAPPY and EDUC. Use a scatter plot and a linear regression model to
examine whether more educated people appear to be happier people. Report all results
and test the relevant hypothesis.
The regression results suggests that more educated people are happier. The
slope coefficient is significantly larger than zero and based on F, the regression
model is deemed significant.
The five countries that appear to be unusually happy are brazil,costa rica,
denmark, finland and norway
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