Question

The following table was generated from the sample data of 10 newborn babies regarding the weight of the mother at birth, the weight of the father at birth, and the weight of the baby at birth. The dependent variable is the weight of the baby, the first independent variable (x1) is the mother's weight, and the second independent variable (x2) is the father's weight.

Intercept   -1.481534   1.398469   -1.059398   0.324599
Mother's Weight   0.129261   0.213314   0.605969   0.563660
Father's Weight   0.998580   0.221601   4.506212   0.002778

Step 1 of 2: Write the multiple regression equation for the computer output given. Round your answers to three decimal places.

Step 2 of 2: Indicate if any of the independent variables could be eliminated at the 0.05 level of significance.

Answer 1

Step 1: Multiple Regression Equation

where Y_hat is the predicted weight of baby at birth

X1:  is the mother's weight

X2:  is the father's weight.

Step 2:

We test the significance of independent variables by hypothesis test, wherein Null hypothesis is that variable is zero and not significant while the alternate hypothesis is that variable is significant

If the p-value is less than the given alpha, 0.05, we reject the null hypothesis and conclude that the variable is significant

For X1, mothers weight

p-value = 0.563660, which is higher than 0.05. So, Mother's weight is not significant

For X2, the father's weight

p-value =0.002778, which is less than 0.05. So, father's weight is significant

So, we can eliminate Mother's weight