Please give a detailed answer Solving process Thank you Is

Please give a detailed answer !! Solving process. Thank you.

Is a company s reputation, a subjective assessment, related to objective measures of corporate performance such as its profitability? One study of this relationship examined the records of 154 Fortune 500 firms. Corporate reputation was measured on a scale of 1 to 10 by a Fortune magazine survey. Profitability was defined as the rate of return on invested capital. The figure below contains Excel output for the regression of profitability (PROFIT) on reputation score (REPUTAT). You can take it as given that examination of the data shows no serious violations of the conditions required for regression inference. Suppose that the mean repudiation score of the 154 companies is 7.678. Give a 95% confidence interval for the mean profitability (return on investment) for all companies with reputation score 7. A company not covered by the Fortune survey has reputation score 7. Will a 95% prediction interval for this companies profitability be wider or narrower than the confidence interval found in the previous exercise? Explain why we should expect this. Then give the 95% prediction interval.

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