Question

6. Given that the dependent variable is SAT score, Create a regression formula from the following output. Also, describe any concerns you have with the model. SUMMARY OUTPUT Regression Statistics - Multiple Re 0.64 R Square 0.40 Adjusted R Square 0.36 Standard Error 86.37 Observations 30.00 ANOVA df F Significance F 0.00 9.17 Regressione Residual Total 2 27 29 SS MS 136783.59 68391.79 201400.58 7459.28 338184.17 Intercept GPA- Femalee Coefficients StandardErrort Stat p-value Lower 95% 364.35 75.24 4.84 0.00 209.98 86.63 22.01 3.94 0.00 41.47 0.80 35.10 0.02 0.98 -71.22

Answer 1

TOPIC:Regression equation.

6.7 que pegression formula is - A y = 364.35 + 86.634 +0.80 22 - where y a predicted SAT score; x = GPA seore; 12 = Dummy variable, where x, { 1 is the person is Jemale lo ;id mare. & coefficient of GPA = 86.63, " Female = 0.80 y-Intercept is = 3 364.35.. -> Concerns regarding the regression equation is we know, R² = coefficient of determination which measures the amount of variation in the dependent variable, explained by the variation of the independent variable.cat The If the value of R² is close to 1, then the dit is considered to be very good. But, here R² is 0.40, which is not close to 1. 2 So, here the dit of the negression equation is not good.

i Again, while considesing the independent variable x2 (Female), we see that, the P-value of the significance of the begression coefficient, comes out to be 0.98. Since the P-value is very much higher than & (=0.05, say, the negression coefficient for X₂ is not significant. so including uz in the negression equation, does not provide a good fit of the negression equation. [And