Question

Consider the following regression run in R, which uses engine size in liters, horsepower, weight, and domestic vs foreign manufacturer to predict mileage:

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> summary(lm(highwaympg~displacement+hp+weight+domestic))

Call:

lm(formula = highwaympg ~ displacement + hp + weight + domestic)

Residuals:

    Min      1Q  Median      3Q     Max

-6.9530 -1.6997 -0.1708 1.6452 11.4028

Coefficients:

              Estimate Std. Error t value Pr(>|t|)   

(Intercept) 53.849794   2.090657 25.757 < 2e-16 ***

displacement 1.460873   0.748837   1.951   0.0543 .

hp           -0.009802   0.011356 -0.863   0.3904   

weight       -0.008700   0.001094 -7.951 6.23e-12 ***

domestic     -0.939918   0.762175 -1.233   0.2208   

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.088 on 87 degrees of freedom

Multiple R-squared: 0.6807, Adjusted R-squared: 0.666

F-statistic: 46.36 on 4 and 87 DF, p-value: < 2.2e-16

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Can you reject a null hypothesis that all true coefficients are zero? What tells you this?

Answer 1

We cannot reject a null hypothesis that all true coefficients are zero.

displacement

p value = 0.0543 .

p-value>α, Do not Reject null hypothesis

  

hp           

p value = 0.3904   

p-value>α, Do not Reject null hypothesis   

weight

p value = 6.23e-12 = 0/0000

p-value<α,Reject null hypothesis

domestic

p value = 0.2208   

p-value>α, Do not Reject null hypothesis   

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