Year Year Quarter Sales Advertising 1 1 144 41 2 151 51 3 134 32 4 151 45 2 1 14

Question

Year

Year

Quarter Sales Advertising 1 1 144 41 2 151 51 3 134 32 4 151 45 2 1 145 48 2 145 34 3 141 29 4 166 43 3 1 151 40 2 164 51 3 151 39 4 176 54 4 1 170 41 2 180 52 3 156 48 4 187 47 5 1 166 44 2 182 48 3 154 44 4 169 36 Run a regression model for the above data a) interprete the meaning of the sample intercept, sample slope, and coefficient of determination b) Is the overall model significant? c) Is the slope term significant? Are the two variables significant, which one is more significant?

Explanation / Answer

Using Minitab:

Regression Analysis: Sales versus Advertising

Analysis of Variance

Source         DF Adj SS Adj MS F-Value P-Value
Regression      1    1402 1401.5     8.88    0.008
Advertising   1    1402 1401.5     8.88    0.008
Error          18    2841   157.8
Lack-of-Fit 13    1625   125.0     0.51    0.846
Pure Error    5    1217   243.3
Total          19    4243

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
12.5632 33.04%     29.32%      19.62%

Coefficients

Term          Coef SE Coef T-Value P-Value   VIF
Constant     105.2     18.3     5.74    0.000
Advertising 1.245    0.418     2.98    0.008 1.00

Regression Equation

Sales = 105.2 + 1.245 Advertising

b)The p-value for Regression is 0.008, indicating that at least one of the regression coefficients is significantly different than zero. Model is significant.

c) Slope is a significant coefficient (P = 0.008).

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