Question

Consider the following data for a dependent variable y and two independent variables, 21 and 22; for these data SST = 15,198.1, and SSR = 14,174.8. M m + G E D TM H Round your answers to three decimal places. a. Compute R b. Compute RX c. Does the estimated regression equation explain a large amount of the variability in the data? - Select your answer -

Answer 1

The statistical software output for this problem is:

Multiple linear regression results: Dependent Variable: y Independent Variable(s): x1, x2 y = -21.875128 + 1.9359505 x1 + 5.0466136 x2 Parameter estimates: Parameter • Estimate • Std. Err. . Intercept -21.875128 19.278714 1.9359505 0.25577184 5.0466136 1.0240949 Alternative. DF# T-Stat. 0 7 -1.1346777 0 7 7.5690523 # 0 7 4.9278769 P-value 0.2939 0.0001 0.0017 x2 Analysis of variance table for multiple regression model: Source DF SS MS F -stat P-value Model 2 13965.248 6982.6239 39.646577 0.0002 Error 7 1232.8522 176.12174 Total 9 15198.1 Summary of fit: Root MSE: 13.271086 R-squared: 0.9189 R-squared (adjusted): 0.8957

Hence,

a) R² = 0.919

b) R_a² = 0.896

c) Yes, because R² is large