Question

Q3. (15 points) The managing partner of an advertising agency believes that his company's sales are related to the industry sales ($ 1000s). He uses Microsoft Excel to analyze the last 4 years of quarterly data (i.e., n=16) with the following results: Regression Statistics Multiple R 0 .802 R Square - 0.643 Adjusted R Square 0.618 Standard Error SYX Observations 0.9224 ANOVA df 1 14 15 F 25.27 Regression Error Total MS 21.497 0.851 Sig.F 0.000 SS 21.497 11.912 33.409 Predictor Coef Intercept 3.962 Industry 0.040451 StdError 1.440 0.008048 Stat 2.75 5.03 P-value 0.016 0.000 Durbin-Watson Statistic 1.59 a) Write the regression equation (1 points). b) What is the coefficient of determination? Interpret this ? (1 points) Test if there is relationship between the company sales and industry sales c) State the hypothesis. (2 points)

Answer 1

Question (a)

Predicted Company Sales = 3.962 + 0.040451 * Indistry Sales

Question (b)

Coefficient of Determination is the R-square value which is 0.643

It implies that 64.3% of variation in Company Sales data is explained by Industry Sales variable

A good R-square value is the one with value greater than 0.5. Here the R-square value is 0.653 implies the model is a good fit of the fit but not a perfect fit

Question (c)

Null Hypothesis Ho : There exists no linear relationship between Company Sales and Industry Sales which is r = 0

Alternate Hypothesis H1 : There exists linear relationship between Company Sales and Industry Sales which is r $\neq$ 0

Question (d)

The test-statistic is F value from the ANOVA table. Here test-statistic is 25.27

If the test-statistic falls in the crtiical region, we reject the Null Hypothesis else we fail to reject the Null Hypothesis

Question (e)

The p-value of test-statistic is the Significance F value from the ANOVA table which is 0.000

If the p-value of test-statistic or  Significance F value is less than the significance level or $\alpha$ value of 0.05, we reject the Null Hypothesis, else we fail to reject the Null Hypothesis

Here p-value of test-statistic or the Significance F value is 0.000 which is less than 0.05, Hence we reject the Null Hypothesis

So the conclusion is There exists linear relationship between Company Sales and Industry Sales

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