With the aim of predicting the selling price of a house in Newburg Park based on…

With the aim of predicting the selling price of a house in Newburg Park based on the distance the house lies from the beach, we’re examining data for houses sold in Newburg Park in the past year. These data detail the distance (x, in miles) of the house from the beach and the selling price (y, in thousands of dollars) of the house for each of 14 houses. The least-squares regression equation based on the data is y=302.76–4.99x. We’re interested in predicting the price of a new house that is 6 miles from the beach in Newburg Park. We have used the regression equation to make this prediction. We’re also interested in both a prediction interval for the house’s price and a confidence interval for the mean price of houses that are this same distance from the beach in Newburg Park. We have already computed the following for our data: • mean square error (MSE) – 1050.17; .1 (6-x)? – 0.1219, 14 14 i=1 where x1,x2,…,* 14 denote the distances from the beach in the sample, and x denotes their mean. Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below. (If necessary, consult a list of formulas.) Lower limit: 1. What is the 90% confidence interval for the mean selling price (in thousands of dollars) when the distance from the beach is 6 miles? (Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.) Upper limit: 2. Choose one response to answer the question below. Choose one Consider (but do not actually compute) the 90% prediction interval for an individual value for selling price when the distance from the beach is 6 miles. How would the confidence interval computed above compare to this prediction interval (assuming that both intervals are computed from the same sample data)? 3. Choose one response to answer the question below. Choose one For the distance from the beach values in this sample, 2 miles is more extreme than 6 miles is, that is, 2 is farther from the sample mean distance from the beach than 6 is. How would the 90% confidence interval for the mean selling price when the distance from the beach is 2 miles compare to the 90% confidence interval for the mean selling price when the distance from the beach is 6 miles? 2. Choose one response to answer the question below. ✓ Choose one The confidence interval would be positioned to the left of the prediction interval. The confidence interval would be positioned to the right of the prediction interval. The confidence interval would be identical to the prediction interval. The confidence interval would have the same center as, but would be narrower than, the prediction interval. The confidence interval would have the same center as, but would be wider than, the prediction interval. 3. Choose one response to answer the question below. ng price whe n interval ( 3. Choose one response to answer the question below. a ✓ Choose one The interval computed from a distance from the beach of 2 would be wider but have the same center. The interval computed from a distance from the beach of 2 would be narrower but have the same center. The interval computed from a distance from the beach of 2 would be narrower and have a different center The intervals would be identical. The interval computed from a distance from the beach of 2 would be wider and have a different center. ri