### Understanding Regression Intervals for Restaurant SpendingA restaurant owner is considering opening an ethnic cuisine restaurant and is interested in how much people in the target community spend on eating out relative to their incomes. A telephone survey was conducted, and the following regression model was developed for individual respondents, where household income is in $1000's:**EatOut$/wk = 21.36 + 0.294HHIncome**#### a) Interpreting the 95% Prediction IntervalA 95% prediction interval for a customer with a household income of $80,000 is (40.92, 48.84). How should the restaurant owner interpret this interval?- **Option A:** 95% of households with an annual income of $80,000 can be expected to spend between $40.92 and $48.84 on eating out each week.- **Option B:** 95% of surveyed households with an annual income of $80,000 spend between $40.92 and $48.84 on eating out each week.- **Option C:** 95% of all households spend between $40.92 and $48.84 on eating out each week.- **Option D:** There is a 95% chance that the mean amount spent by people with an annual household income of $80,000 is between $40.92 and $48.84.#### b) Interpreting the 95% Confidence Interval for the MeanA 95% confidence interval for the mean amount spent weekly to eat out by people with a household income of $80,000 is (43.55, 46.21). How should the restaurant owner interpret this interval?- **Option A:** It can be stated with 95% confidence that the mean amount spent weekly by individuals whose household incomes are $80,000 is between $43.55 and $46.21.- **Option B:** 95% of all households with an annual income of $80,000 will spend between $43.55 and $46.21 on average.- **Option C:** It can be stated with 95% confidence that the average amount spent each week by households in the survey with an income of $80,000 is between $43.55 and $46.21.- **Option D:** It can be stated with 95% confidence that the sample mean of the amount spent eating out each week by households with an income of $80

A restaurant owner is considering opening an ethnic cuisine restaurant and wonders how much people in the target community spend on eating out relative to their incomes. She commissions a telephone survey and builds the following regression model for individual respondents, where household income is in $1000's. Answer parts a through c. EatOut$/wk=21.36 +0.294HHIncome a) A 95% prediction interval for a customer with a household income of $80,000 is (40.92,48.84). Explain to the restaurant owner how she should interpret this interval. O A. 95% of households with an annual income of $80,000 can be expected to spend between $40.92 and $48.84 eating out each week. O B. 95% of surveyed households with an annual income of $80,000 spend between $40.92 and $48.84 eating out each week. OC. 95% of all households spend between $40.92 and $48.84 to eat out each week. O D. There is a 95% chance that the mean amount spent by people with an annual household income of $80,000 is between $40.92 and $48.84. b) A 95% confidence interval for the mean amount spent weekly to eat out by people with a household income of $80,000 is (43.55,46.21). Explain to the restaurant owner how to interpret this interval. OA. It can be stated with 95% confidence that the mean amount spent weekly by individuals whose household incomes are $80,000 is between $43.55 and $46.21. OB. 95% of all households with an annual income of $80,000 will spend between $43.55 and $46.21 on average. OC. It can be stated with 95% confidence that the average amount spent each week by households in the survey with an income of $80,000 is between $43.55 and $46.21. OD. It can be stated with 95% confidence that the sample mean of the amount spent eating out each week by households with an income of $80,000 is between $43.55 and $46.21. c) Now explain why these intervals are different. O A. Means can be estimated more accurately than values for individuals. That's why the confidence interval for the mean is narrower than the corresponding interval for an individual. OB. Since the p-value for the prediction interval is higher than that of the confidence interval, the prediction interval must be wider to compensate for the added significance. OC. Prediction intervals are affected by outliers in the data more than confidence intervals, so the difference between the two suggests that there are many extreme data points in the sample. O D. Such a large difference between the two intervals indicates that the regression line does not accurately model the data.