Determine Statistical evaluation of regression results - please detail for each

Question

Determine Statistical evaluation of regression results - please detail for each coefficient:

1) T-test: use P-value (also called significance value) to determine test of statistical significance of each estimated coefficient. [If P value < 0.05, the coefficient is significant (or important). If P value > 0.05, the coefficient is insignificant (or unimportant)].

2) R2 (coefficient of determination): percentage of variation in the variable (Y) accounted for by variation in all explanatory variables (Xn) .R2 value ranges from 0.0 to 1.0 . The closer to 1.0, the greater the explanatory power of the regression.

3) F-test: measures statistical significance of the entire regression as a whole (not each coefficient): F-test is not required by this project but it will nice addition if you include this test.

Regression Statistics Multiple R 0.826438926 R Square 0.683001299 Adjusted R Square 0.592430241 Standard Error 0.377626464 Observations 19 ANOVA df SS MS F Significance F Regression 4 4.301470 1.075368 7.541055 0.001860 Residual 14 1.996424 0.142602 Total 18 6.297895 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.446478 1.905209 0.234346 0.818109 -3.639789 4.532746 -3.639789 4.532746 Price ($) -0.015119 0.010284 -1.470238 0.163612 -0.037175 0.006937 -0.037175 0.006937 Advertising ($1000) 0.657420 0.203986 3.222870 0.006135 0.219914 1.094926 0.219914 1.094926 Price X ($) -0.006098 0.022818 -0.267248 0.793175 -0.055038 0.042842 -0.055038 0.042842 Income ($1000) 0.494083 0.195594 2.526061 0.024215 0.074575 0.913592 0.074575 0.913592

Explanation / Answer

1. Soution :Let us check for the coefficient of price first

note we are asuuming that 1.) Ho = 0 and 2.) H1 != 0

1.) H0 = 0 is the null hypothesis for all the coefficient in our model

2.) H1!=0 = This implies H1 is not equal to zero and it is the alternative hypothesis.

Given Coefficient of price = -0.015119 and p- value of price = 0.163612.This p-value of price is greater than the level of significance 0.05.And we accept null hypothesis and reject alternative hypothesis.Hence the coefiicient of price is statistically insiginificant.

The p-value of advertising is 0.006135 which is less than 0.05 hence we reject hence we reject null hypothesis and accept alternative hypothesis.Therefore the coefiicient of advertising is statistically significant.

The p-value of the price X is 0.793175 > 0.05.Accept null hypothesis and accept alternative hypothesis.Hence the price X is statistically insignificant.

The p-value of income 0.024215 < 0.05 .Reject null hypothesis and accept alternative hypothesis.The coefficient of income is statistically insigficant.

Q.2) R2 = Explained sum of squares /Total sum of squares.

=4.301470/6.297895 = 0.6829

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