Question

a.

From the regression output, we know that the regression learned three parameters: the intercept, size (cubic metres) and weight(00's kg).

Let us say our regression equation is of the form:

y = intercept + b1*size + b2*weight

Since intercept, b1 and b2 are known to us, we know:

y= -0.20018 + 2.211198 * size - 0.07185 * weight

Let's discuss each of these parameters:

intercept: The coefficient of this variable is -0.20018. This means that when size are weight are 0, the value of y is -0.20018. This is known as the y-intercept value (or simply intercept) because this is the value at which the regression line cuts the y-axis.

The null hypothesis is that this variable is not significant. We need significant proof to think otherwise. iIf the p value is less than 0.05, then we will reject the null hypothesis.

The p-value is quite high (0.8192); thus we will say that this variable is not significant and the null hypothesis is not rejected.

size: The coefficient of this variable is 2.211198. This means that with every unit change in the size, the value of y changes by ~2.2 units. Here, we assume that the value of other variables is constant.

The null hypothesis is that this variable is not significant. We need significant proof to think otherwise. iIf the p value is less than 0.05, then we will reject the null hypothesis.

The p-value is quite low (0.0136); thus we will say that this variable is significant and the null hypothesis is rejected.

size: The coefficient of this variable is -0.07185. This means that with every unit change in the size, the value of y changes by ~-0.07 units. Here, we assume that the value of other variables is constant.

The null hypothesis is that this variable is not significant. We need significant proof to think otherwise. iIf the p value is less than 0.05, then we will reject the null hypothesis.

The p-value is quite high (0.6845); thus we will say that this variable is not significant and the null hypothesis is not rejected.

b.

The correlation matrix has not been given. Please update the question or send me the correlation matrix in the comments, and I will update this part of the answer.

Happy learning!

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