Assignment #7 Multiple Regression Analysis

Develop a model to predict average industry demand using the following:

Click here to see data set

The items are highly correlated with our Y variable of average industry demand.

To view correlation please click here.

Our multiple regression equation is:

Y1 = 15475.97 - 39.3095 X1 (average price) + 0.0030 X2 (average industry advertising) - 00045X3

(Average Advertising One Quarter Ago) + 0.0130 X4 (Average R&D Expenditures, One Quarter

Ago) + 0.0030 X5 (Average Advertising Two Quarters Ago) + 0.0314 X6 (Average R&D

Expenditures, Two Quarters Ago)

Test for Overall Significance:

H0 : b 1 = b 2 = b 3 = b 4 = b 5 = b 6 = (There is no linear relationship between the dependent variable and the explanatory variable)

H1 : b j ¹ 0 (At least one regression coefficient is not equal to 0)

If a level of significance of .05 is chosen, then we determined the critical value on the F distribution with 6 and 15 degrees of freedom is 2.79. From our multiple regression analysis we determined the F statistic is 1.074. Since F = 1.074 < Fu(6,15) = 2.79, so we can accept H0 because there is no linear relationship between the dependent variable and explanatory variables.

To view multiple regression model click here

Test for Individual Significance:

X1 Average Price

H0 : b 1 = 0 (there is no evidence that X1 (Average Price) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = -1.361 > -t15 = -1.7823, so we can accept H0 because there is no evidence that the variable X1 (Average Price) contributes to the model.

X2 Average Industry Advertising

H0 : b 1 = 0 (there is no evidence that X2 (Average Industry Advertising) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = 0.5025 < t15 = 1.7823, so we can accept H0 because there is no evidence that the variable X2 (Average Industry Advertising) contributes to the model.

X3 Average Advertising One Quarter Ago

H0 : b 1 = 0 (there is no evidence that X3 (Average Advertising One Quarter Ago) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = -0.74893 < -t15 = -1.7823, so we can accept H0 because there is no evidence that the variable X2 (Average Industry Advertising) contributes to the model.

X4 Average R & D Expenditures, One Quarter Ago

H0 : b 1 = 0 (there is no evidence that X4 (Average R & D Expenditures, One Quarter Ago) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = 0.97719 < t15 = 1.7823, so we can accept H0 because there is no evidence that the variable (Average R & D Expenditures, One Quarter Ago) contributes to the model.

X5 Average Advertising Two Quarters Ago

H0 : b 1 = 0 (there is no evidence that X5 (Average Advertising Two Quarters Ago) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = 0.520073 < t15 = 1.7823, so we can accept H0 because there is no evidence that the variable (Average Advertising Two Quarters Ago) contributes to the model.

X6 Average R & D Expenditures, Two Quarters Ago

H0 : b 1 = 0 (there is no evidence that X6 (Average R & D Expenditures, Two Quarters Ago) significantly contributes to the model)

H1 : b j ¹ 0 (X1 significantly contributes to the model)

If a level of significance of .05 is chosen, then the critical value of t with 15 degrees of freedom is -1.7823 and 1.7823.

t = 0.388882 < t15 = 1.7823, so we can accept H0 because there is no evidence that the variable (Average R & D Expenditures, One Quarter Ago) contributes to the model.