Question

Problem. Gwyneth Paltrow wants to develop a simple linear regression model, X. = Bo + Boxi + Ej, to predict the total sum of money in $1,000) customers withdraw from automatic teller machines (ATMs) on a weekend (vi) based on the median value of homes in the vicinity of the ATMs (xi). She asked for your help with the following Excel printout: df Sum of Squares Mean Square F Significance F Regression 10.56 0.01 528 50 Residual 528 450 978 9 10 Total Coefficients Standard Error + Stat P-value Lower 95% Upper 95% Intercept 1131 Home value X 500 20 2.262 0.05 3.250 0.01 -0.079 2262.079 ? ?

What is the sample correlation coefficient r_xy between x_i and y_i?

Find the 95% confidence interval for the regression coefficient β₁.

Test at a 0.05 level of significance to determine whether the regression coefficient β₁ is larger than 20.

- Alternatives

-Decision Rules

-Conclusion

Answer 1

+7 corelation = R R?= SSR SST 528 978 - R²=0.54 R = 10.54 = 0.73 R = 0.73 22 ß I (tcostical) (SE) tch-2,0.05) = 18, 0005) = 2.306 But here we dont know the Weffucut so - GO Estat = wefficient SE 3.250 = efficent 20 (20) (3.250) = coefficient 65 = efficient = 65+ (2.306) (20) = (65+ 46.12) = (18.88, 111.12)

Page No - Ho: 8, 520, H: 8,320 we have computed 951. CI (18.88, 111.12) This C.I containe 20 in iz so B, is statistically fignificant