Answer
There is not enough evidence to conclude that there is a linear relation between sugar and calories.
There is enough evidence to conclude that there is a linear relation between fat, protein and carbs with calories.
We need to remove the explanatory variable sugar from the model.
Work Step by Step
1) $H_0: β_1=0$ versus $H_1: β_1\ne0$
$t_0=37.49$ with a P-value $\lt0.001\ltα=0.05$. Reject the null hypothesis.
2) $H_0: β_2=0$ versus $H_1: β_2\ne0$
$t_0=7.53$ with a P-value $=0.005\ltα=0.05$. Reject the null hypothesis.
3) $H_0: β_3=0$ versus $H_1: β_3\ne0$
$t_0=1.34$ with a P-value $=0.273\gtα$. Do not reject the null hypothesis.
4) $H_0: β_4=0$ versus $H_1: β_4\ne0$
$t_0=11.60$ with a P-value $=0.001\ltα=0.05$. Reject the null hypothesis
