Extra Problems, Set #2 Regression Analysis
Consider the following data
Sales
Adv
Yi
Xi
3
4
6
5
7
6
5
9
10
9
1
2
3
4
5
6
7
8
9
10
1. Input this data on a spreadsheet. Using the regression option, generate regression
predictions. Write your results as an equation, as we did in class. In particular, write
(a) write the regression equation, with estimated coefficients,
(b) below the regression equation, list in parentheses the standard errors of the coefficient
estimates
(c) To the right of the estimated equation write
i) R2 and adjusted R2
ii) F test statistic, along with its p value
iii) MSE of the estimate.
2. Multivariate Regression. Now add to your above regression in a price variable, with
values: 8, 7.5, 7.25, 7.25, 6, 6.75, 6, 5, 4.4, 5.2. Estimate the new regression equation.
Print regression results. Write out the estimated demand function, as in part (c) above.
.
3. Evaluating regression results. With the data you generated in (2) above do the
following.
a. Interpret the R2.
b. What is the difference between R2 and adjusted R2?
c. Goodness of Fit Test. Looking at the F test statistic, can you conclude that the
regression estimate explains more of the variation in sales than the simple
average of sales? Explain.
d. For each coefficient, write the 95% confidence intervals about the estimates.
From this data, which parameters are significant explainers of sales?
e. Observe that we can do the same exercises with this information that we did
previously. In particular, suppose that advertising expenditures are 10 and that the
current price is $6. Calculate the point price elasticity of demand.
4. Transform the data you created in question 7 to estimate the equation
ln Y
=
a
+
b ln A + c ln P
a. Print regression results, following the style you used in equation 1(c).
b. Calculate the price elasticity of demand for this equation.
c. At a 95% confidence level, can you conclude that the firm is at the point of
unitary elasticity?
d. What is the advertising elasticity of demand? How confident can you be that
advertising increases sales? Justify your answer.