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Sagot :
The regression analysis evaluates the amount of relationship that exists
between the variables in the analysis.
- The regression equation is; [tex]\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}[/tex]
- 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;
[tex]\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][/tex]
The least squares regression equation is; [tex]\overline y = b \cdot \overline x + c[/tex]
Where;
[tex]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 }}[/tex]
[tex]\overline y[/tex] = The mean crash fatality = 15.52
[tex]\overline x[/tex] = The mean lemon import = 373.6
Therefore;
[tex]b = \dfrac{-171.36 }{67093.2 } = -0.00255[/tex]
c = [tex]\overline y[/tex] - b·[tex]\overline x[/tex] = 15.52 - (-0.00255)×373.6 = 16.47268
Therefore;
- The regression equation is [tex]\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}[/tex]
Second part;
When the imports is 425 metric tons of lemon, we have;
[tex]\overline y[/tex] = -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
The prediction is worthwhile
Learn more about regression equation here:
https://brainly.com/question/5586207
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