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A regression line shows how an explanatory variable $x$ affects a response variable $y$ You can use a regression line to forecast the value of $y$ for any value of $x$ by plugging this $x$ into the equation of the line.

The scatter plot for the given data is as follows

We can see from the scatter plot that all points have a linear rising trend. As a result, we can conclude that there is a positive relationship between age and height. To put it another way, Age and Height are positively connected.

As a result, a scatterplot is created.

The explanatory variable is "age," while the response variable is "height." The output of the least-square regression line using MINITAB is as follows.

Analysis of Regression: Age versus Height

From the above output, the least-square regression line is given by

$Height=71.95+0.0383Age$

Hence, the least-square regression line is $Height=71.95+0.0383Age$

Part (b) yields the following regression line between Age and Height:

$Height=71.95+0.0383Age$

We can anticipate Sarah's height at $40$years old using the regression line shown above ($480$months) That means, Sarah's height at $40$years ($480$months) is expected to be, $\stackrel{Áåœ}{Y}=71.95+0.383×480$

$$\begin{gathered} =255.94984cm \\ =\frac{255.94984}{2.54}inches(\mathrm{\backslash 1}inch=2.54cm) \end{gathered}$$

$$\begin{gathered} =100.7677inches \\ =255.94984cm \\ =100.7677inches \end{gathered}$$

The age of $40$ years ($480$ months) is well outside the range of our data's $X-$ values. At such extreme levels, we can't say whether the relationship remains linear. Predicting Sarah's height at $40$ years old ($480$ months) is an extension of the connection beyond the data. As a result, we can conclude that the estimated height is inaccurate.