91Ó°ÊÓ

It is given in the question that:

$$\begin{gathered} \stackrel{Áåœ}{y}=170+11.8x \\ \stackrel{Áåœ}{y}=88+24.5x \end{gathered}$$

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

The regression line for drink products is substantially steeper than the regression line for food goods, as shown in the scatterplot. The equations of the regression lines confirm this because $24.5$ is substantially greater than $11.8$ In the equations of the regression lines, $170$ is substantially higher than $88$ hence the intercept of the food goods is much greater than the intercept of the drink products. This is also seen in the scatterplot, where the regression line for food goods is higher on the left side of the graph than the regression line for drink products.

It is given in the question:

$$\begin{gathered} \stackrel{Áåœ}{y}=170+11.8x \\ \stackrel{Áåœ}{y}=88+24.5x \end{gathered}$$

As a result, the number of calories we should expect to discover in a food item containing $5$grams of fat is estimated as follows:

$$\begin{gathered} \stackrel{Áåœ}{y}=170+11.8x \\ =170+11.8\left(5\right) \\ =229 \end{gathered}$$

And the number of calories in a food item containing $5$grams of fat is calculated as follows:

$$\begin{gathered} \stackrel{Áåœ}{y}=88+24.5x \\ =88+24.5\left(5\right) \\ =210.5 \end{gathered}$$

Now, the difference between the two predicted values is:

$$\begin{gathered} =229−210.5 \\ =18.5 \end{gathered}$$

This means that a food item containing $5$grams of fat will contain $18.5$calories more than a drink containing $5$ grams of fat.