Question

Problem. Hayley Westenra wants to develop a simple linear regression model, y = B. + B.X + E, to predict the selling price of a house in the greater Baton Rouge area (Y) based on the size of its living area in square feet (x). She asked for your help with the following Excel printout: Mean Square F 7.56 Significance F 0.01 Regression Residual df 1 30 31 Sum of Squares 121 480 601 Total Coefficients 163750 Standard Errort Stat 125000 1.310 24 2.750 Intercept Size X P-value 0.2000 0.0100 Lower 95% -91534.1 ? Upper 95% 419034.1 (1) What is the sample correlation coefficient between x and y? Select one: or=0.7944 None of the other four Orx=0.5825 OP = 0.6705 O 16 = 0.3598 (2) Find the 95% confidence interval for the regression coefficient B.. Select one: 16.99 - 115.01 10.25 - 121.75 20.99 - 111.01 36.99 -95.01 None of the other four

(3) Test, at a 0.05 level of significance, the alternate hypothesis that the average price per square feet is more than $30 in the greater Baton Rouge area.

Answer 1

0 None of the other four coeficient of determination : 12 SS (Regrenion) SS(Total) = 121 :- ray = 54301 = 0.44869 ~ 0.4487 16.99-115.011 ß, = (t Stat) ( standard error) = (2.750)(24) = 66 de 1-0.95=0.05; dof (Residual) = 30 critical value, tal = 2.042 (two-tailed) i confidence interval = Ô t tale (std. error) = 66 $ 2.042 *( 24) = (16.992-115.008) ~ 16.99-115.01 BHO: . 330 Hii ß. >301 (i) eritical value, ta=1.697 (one tailed) If t* < 1,697, conclude Ho i otherwise, conclude Hi None of the other four 66-30 24 (ii) Test Statistic, tt - Bi-Mi Std. error * = 1,500 (iv) conclude Ho that ß, is no larger than $301