The regression analysis evaluates the amount of relationship that exists
between the variables in the analysis.
- The regression equation is;
![\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Coverline%20y%20%3D%20-0.00255%20%5Ccdot%20%5Coverline%20x%20%2B%2016.47268%7D)
- The prediction is worthwhile because it gives an idea of the observed Crash Fatality Rate and it is therefore approximately correct.
Reasons:
First part;
The given data is presented as follows;
![\begin{tabular}{|cc|c|}Lemon Imports (x) &&Crash Fatality Rate\\232&&16\\268&&15.7\\361&&15.4\\472&&15.5\\535&&15\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%7B%7Ccc%7Cc%7C%7DLemon%20Imports%20%28x%29%20%26%26Crash%20Fatality%20Rate%5C%5C232%26%2616%5C%5C268%26%2615.7%5C%5C361%26%2615.4%5C%5C472%26%2615.5%5C%5C535%26%2615%5Cend%7Barray%7D%5Cright%5D)
The least squares regression equation is; ![\overline y = b \cdot \overline x + c](https://tex.z-dn.net/?f=%5Coverline%20y%20%3D%20%20b%20%5Ccdot%20%5Coverline%20x%20%2B%20c)
Where;
![b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}](https://tex.z-dn.net/?f=b%20%3D%20%5Cmathbf%7B%5Cdfrac%7B%5Csum%20%5Cleft%28x_i%20-%20%5Cbar%20x%5Cright%29%20%5Ctimes%20%5Cleft%28y_i%20-%20%5Cbar%20y%5Cright%29%20%7D%7B%5Csum%20%5Cleft%28x_i%20-%20%5Cbar%20x%5Cright%20%29%5E2%20%7D%7D)
= The mean crash fatality = 15.52
= The mean lemon import = 373.6
Therefore;
![b = \dfrac{-171.36 }{67093.2 } = -0.00255](https://tex.z-dn.net/?f=b%20%3D%20%5Cdfrac%7B-171.36%20%7D%7B67093.2%20%7D%20%3D%20-0.00255)
c =
- b·
= 15.52 - (-0.00255)×373.6 = 16.47268
Therefore;
- The regression equation is
![\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Coverline%20y%20%3D%20-0.00255%20%5Ccdot%20%5Coverline%20x%20%2B%2016.47268%7D)
Second part;
When the imports is 425 metric tons of lemon, we have;
= -0.00255 × 425 + 16.47268 = 15.38893 ≈ 15.4
Therefore;
When the import is 425 metric tons, the Crash Fatality Rate ≈ 15.4
Given that the predicted value is between the values for 268 and 535, we
have that the prediction is approximately correct or worthwhile
<u>The prediction is worthwhile</u>
Learn more about regression equation here:
brainly.com/question/5586207