In order to study the relationship of advertising and capital investment with co

Question

In order to study the relationship of advertising and capital investment with corporate profits, the following data (in $100,000) were collected for 10 firms in the same year. The variable Y represents profit for the year, X1 represents capital investment, and, X2 represents advertising expenditures.

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*round answersto 4 decimal places if possible

ANSWER THE FOLLOWING:

1.) S = ?

2.) When X1 = 16, X2 = 2 ,then y-hat = ?

3.) Residual = ?

4.) What is the 95% PI for Y?

5.) What is the 95% confidence interval for E(y)?

6.) In testing if X2 is significant, what is the value of the test statistic?

7.) In testing if X2 is significant, what is the correct decision and conclusion?

Linear Regression Model Number of Observations Read 10 Number of Observations Used 10 Analysis of variance Source DF Sum of Mean F Value Pr F Squares Square Model 2 355.2151 177.6075 16.28 0.002 Error 7 76.38486 10.91212 Corrected Total 9 431.6000 Root MSE 3.30335 R-Square 0.8230 Dependent Mean 9.80000 Adj R-Sg 0.7725 Coeff Var 33.70766 Parameter Estimates Variable DF Parameter Standard t Value Pr It 95% Confidence Limits Estimate Error Intercept 1 -8.17702 4.20599 -1.94 0.0930 -18.12260 1.76856 X1 1 0.29213 0.13571 2.15 0.0684 -0.02878 0.61304 X2 1 4.43430 0.80024 5.54 0.0009 2.54203 6.32658

Explanation / Answer

`1. S = 3.30335

2. Given X1 = 16, X2 = 2

Ycap = -8.17702+0.29213X1 + 4.43430X2

=  -8.17702+0.29213(16) + 4.43430(2) = 5.36566

3.

Residual = 2 - 5.36566 = -3.36566

6: Test statistc

t = 5.54

P-value 0.0009

7. Here P value < alpha 0.05, we reject H0

There is significant of the variable X2 on the regression line

i.e. the population regression coefficient value is not equal to zero.

t =

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