Answer
There is not enough evidence to conclude that there is a linear relation between protein and calories.
There is enough evidence to conclude that there is a linear relation between fat and carbohydrate with calories.
We need to remove the explanatory variable protein from the model.
Work Step by Step
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
See the results obtained in item (b)
$t_0=-0.15$ with a P-value $=0.881\gtα=0.05$. Do not reject the null hypothesis.
2) $H_0: β_2=0$ versus $H_1: β_2\ne0$
See the results obtained in item (b)
$t_0=2.85$ with a P-value $=0.021\ltα=0.05$. Reject the null hypothesis.
3) $H_0: β_3=0$ versus $H_1: β_3\ne0$
See the results obtained in item (b)
$t_0=3.72$ with a P-value $=0.006\ltα=0.05$. Reject the null hypothesis.
