# Regression analysis

The following questions refer to this regression equation. (Standard errors in parentheses.)

QD = 15,000 - 10 P + 1500 A + 4 PX + 2 I, (5,234) (2.29) (525) (1.75) (1.5)

R2 = 0.65

N = 120

F = 35.25

Standard error of Y estimate = 565

Q = Quantity demanded

P = Price = 7,000

A = Advertising expense, in thousands = 54

PX = price of competitor's product = 8,000

I = average monthly income =4,000

2) How is the R2 value calculated, and what information does this give you?

3) When would you use a one-tailed rather than a two-tailed t-test when checking significance levels?

4) What is multicollinearity? In general, how would you know if you had a problem with multicollinearity, and how could you correct it?

7) Explain the difference between Cross-Section and Time-Series Regression Analysis.

#### Solution Preview

The following questions refer to this regression equation. (Standard errors in parentheses.)

QD = 15,000 - 10 P + 1500 A + 4 PX + 2 I, (5,234) (2.29) (525) (1.75) (1.5)

R2 = 0.65

N = 120

F = 35.25

Standard error of Y estimate = 565

Q = Quantity demanded

P = Price = 7,000

A = Advertising expense, in thousands = 54

PX = price of competitor's product = 8,000

I = average monthly income =4,000

2) How is the R2 value calculated, and what information does this give you?

One of the two most important statistics (the other is the residual standard deviation) for assessing how well regression succeeds in estimating/predicting the response. R-square has two important interpretations:

1) R-square = square of correlation between the response and the predictor. This is the same as the square of the correlation between the response and the FITs Thus, the larger R-square, the more closely the FITs correspond to the ACTUALs. If R-square = 1, then the FITs equal the ACTUALs, and all of the data points lie exactly on the regression line, and all of the residuals are 0, and s = 0. If R-square = 0, then the regression line is a horizontal line with slope = 0 and intercept = mean of Y. And if the regression line is horizontal, then the estimated value of Y (the FIT) is the same for any X (namely, FIT = mean of Y), so the estimated Y does not depend on X (b/c the estimate is the same for all X), so X offers us no information about Y - i.e., Y and X are ...

#### Solution Summary

The solution provides detailed explanation about regression such as calculating the R2, multi-collinearity, cross sectional and time series data etc.