Question 37 5 pts What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between 3; = diamond price (in dollars) and a: = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Predictor Variables Coefcient Std Error T P Constant 2298.36 158.531 14.50 0.0000 Size 11598.9 230.111 50.41 0.0000 RSquared 0.8925 Resid. Mean Square (MSE) 1248950 Adjusted R-Squared 0.8922 Standard Deviation 1 11 7.56 The model was then used to create 95% condence and prediction intervals for y and for E(Y) when the carat size of the diamond was 1 carat. The results are shown here: 95% condence interval for mean y: ($9091.60, $9509.40) 95% prediction interval for an individual y: ($7091.50, $11,510.00) Which of the following interpretations is correct if you want to use the model to determine the price of a single 1-carat diamond? We are 95% condent that the average price of all 1-carat diamonds will fall between $9091.60 and $9509.40. We are 95% condent that the price of a 1-carat diamond will fall between $9091.60 and $9509.40. We are 95% condent that the average price of all 1-carat diamonds will fall between $7091.50 and $11,510.00. We are 95% condent that the price of a 1-carat diamond will fall between $7091.50 and $11,510.00. Question 38 10 pts A manager at a car wash company in Missouri wants to measure the effectiveness of price discounts and various types of advertisement expenditure on sales. For the analysis, he uses varying price discounts (DISCOUNT) and advertising expenditures on radio (RADIO) and newspapers (NEWSPAPER) in 40 counties in Missouri. The manager would like to test if the advertising expenditures on radio and newspapers have a statistically signicant inuence on sales. She decides to use the Partial F-test. First, she runs the full model Sales = 30 l [31 Discount l 32 Radio I BgNewspaper + a The JMP output from the full model is shown below. A Summary of Fit l RSquare 0.640357 RSquare Adj 0.610387 Root Mean Square Error 5.793039 Mean of Response 54.59725 Observations (or Sum Wgts) 40 A Analysis of Variance Sum of Source DF Squares Mean Square F Ratio Model 3 2151.1298 717.043 21.3665 Error 36 1208.1348 33.559 Prob > F C. Total 39 33592646 <.0001 next she runs the reduced model sales="Bo" discount e jmp output from is shown below. summary of fit rsquare adj root mean square error response observations sum wgts analysis variance source df squares f ratio prob> F C. Total 39 3359.2646 <.0001 the value of partial f statistic is:>