Quiz 6: Simple Linear Regression

Business

Identify which of the given situations is inconsistent. Incorrect option: Option (a) img and img The above situation is consistent. Reason: Here, the regression coefficient is img and the correlation coefficient is img which has same sign. Incorrect option: Option (c) img and img The above situation is consistent. Reason: Here, the regression coefficient is img and the correlation coefficient is img which have same sign. Incorrect option: Option (d) img and img The above situation is consistent. Reason: Here, the regression coefficient is img and the correlation coefficient is img which have same sign. Correct option: Option (b): img and img The above situation is inconsistent. Reason: From the above equation, the regression coefficient is img and the correlation coefficient is img which have different sign.

a. Interpret the slope img of the regression equation. The regression equation is, img Here, img = Earnings, in billions of dollars and img = GNP (gross national product), in billions of dollars. From the regression equation, the slope img is img . Interpretation: The estimated earnings will increase by 0.06 billion of dollars as the GNP is increased by 1 billion of dollars. In other words, for each increase of 1 billion of dollars in the GNP increases the estimated earnings by 0.06 billion of dollars. b. Interpret the Y -intercept img of the regression equation. From the above regression equation, the Y -intercept img is img . Interpretation: The estimated earnings will be 0.078 billion of dollars when the GNP is 0 billion of dollars.

a. Check whether or not there is a significant relationship between weekly advertising expenditures ( X ) and weekly sales ( Y ). The hypotheses are given below: Null hypothesis: img That is, there is no linear relationship between weekly advertising expenditures and weekly sales. Alternative hypothesis: img That is, there is a linear relationship between weekly advertising expenditures and weekly sales. Obtain the prediction equation by using the MINITAB.\ MINITAB procedure: Step 1: Choose Stat Regression Regression. Step 2: In the Response box , enter the Y variable as Sales from the box on the left. Step 3: In the Predictors box , enter the X variable as Expend from the box on the left. Step 4: Click OK. MINITAB output: img From the above MINITAB output, the value of F -ratio is img and the corresponding p -value is img . Conclusion: Here, img is 0.002, which is lesser than any level of significance img . Therefore, by the rejection rule, reject the null hypothesis img . Thus, it can be concluded that there is an evidence to reject the null hypothesis img at any level of significance img . Hence, there is a linear relationship between weekly advertising expenditures and weekly sales. b. State the prediction equation. From the above MINITAB output, the prediction equation is img …… (1) Here, img = Sales, img = Expenditure c. Forecast the sales for an advertising expenditure of $50. Substitute img in equation (1) img Thus, the forecasted sales for an advertising expenditure of $50 is img . d. Obtain the percentage of the variation in sales can be explained with the prediction equation. From the above MINITAB output, the coefficient of determination, img is 0.719. Thus, img of variation in sales can be explained with the prediction equation. e. Obtain the amount of unexplained variation. From the above MINITAB output, the value of SSE is 36,121. Thus, the amount of unexplained variation is img . f. Obtain the amount of total variation. From the above MINITAB output, the value of SST is 128,552. Thus, the amount of total variation is img .