Question

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.)

Answer 1

(3) For An = 6, j = 302.76 – (4.99 x 6) = 272,82 Nowy tarzin-z = toos, 12 = Also, I + (an- x² + (bn) : Ź (ou - ū)? 0.1219 14 + = Grinõusz .1 MSE= 1050.17 ..90% e confidence intervala Yu (tal;n-2)/MSE (1 + (n -x] lown limit = 252.65 Upps limita 292.99 - 4th option (3) 3rd option (If this is wrong, mark the 5th option. I