A regression was run on the variable SPEED with explanatory varaibles: TOP, WEIG

Question

A regression was run on the variable SPEED with explanatory varaibles: TOP, WEIGHT, and HP. Answer the following with the information below:

What is the estimated equation of the regression?

Interpret each of the regression coefficients.

. regress SPEED TOP WEIGHT HP 30 79.15 0.0000 0.9013 0.8899 11.034 Source df MS Number of obs F (3, 26) Prob > F Model 28909.3764 3165.3236 Residual 26 121.743215 R-squared Adj R-suared - Total 32074.7 29 1106.02414 Root MSE SPEED Coef Std. Err t >It (95% Conf. Interval] TOP WEIGHT HP cons 0.28 0.784 -2.81 0.009 13.19 0.000 12.65 0.000 -10.50486 1.637827 5.907327 .0064487 .0124824 137.6644 10.87953 13.78051 -.0313813 -.0048702 .1902891 160.0276 -.0181258 . .1646311.0 .1389731 115.3012

Explanation / Answer

estimated equation of the regression

Speed = 137.6644 + 1.6378*TOP - 0.0181*WEIGHT + 0.1646*HP

Interpretation:

Regression coefficients represent the mean change in the response variable (Speed) for one unit of change in the predictor variables ( TOP, WEIGHT, and HP) while holding other predictors in the model constant.

Constant ( Intercept) : We would expect an average speed of 137.6644 in partial sun with no predictor variables in model. However, this is only a meaningful interpretation if it is reasonable that all regressor variables can be 0.

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