(2) What is the proportion of operating income exceeding 175?

6. An international business uses a simple linear regression model to estimate the relationship between the number of advertisements X and the sales amount Y. According to the monthly data of the business from January to October, 111, the average value of the 10 sales is 130, while the variation is 1748. As for the average number of 10 advertisements, it is 14. Additionally, the covariance between the sales amount Y and the number of advertisements X is 316. Also, the regression equation estimated using the classical least squares method (OLS) is: Y = 60 + 5X. Please answer: (25 %) (1) If the sales amount in March is 88, and the number of advertisements in this month is 8. Please estimate the fitted value for the sales amount on March, 111.

(2) Continuing from the previous question, please estimate the residual value of the sales amount in March.

(3) Estimate the coefficient of determination \((\mathbb{R}^2)\).

(4) Please estimate the correlation coefficient (CORR) between the sales amount Y and the number of advertisements X.

(5) In the case that the significant level alpha \((\alpha)\) is equal to 0.05, please use the T test approach to test the hypothesis that the number of advertisements X affects the sales amount Y. That is, please check whether the slope value of the regression linear relationship is zero or not.

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