Question

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Using the listed​ lemon/crash data, where lemon imports are in metric tons and the fatality rates are per​ 100,000 people, find the best-predicted crash fatality rate for a year in which there are 425 metric tons of lemon imports. Is the prediction​ worthwhile?
Lemon Imports Crash Fatality Rate
232 16
268 15.7
361 15.4
472 15.5
535 15

Answer 1

The regression analysis evaluates the amount of relationship that exists

between the variables in the analysis.

• The regression equation is; $\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}$

• 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;

$\begin{tabular}{|cc|c|}Lemon Imports (x) &&Crash Fatality Rate\\232&&16\\268&&15.7\\361&&15.4\\472&&15.5\\535&&15\end{array}\right]$

The least squares regression equation is; $\overline y = b \cdot \overline x + c$

Where;

$b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}$

$\overline y$ = The mean crash fatality = 15.52

$\overline x$ = The mean lemon import = 373.6

Therefore;

$b = \dfrac{-171.36 }{67093.2 } = -0.00255$

c = $\overline y$ - b·$\overline x$ = 15.52 - (-0.00255)×373.6 = 16.47268

Therefore;

• The regression equation is $\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}$

Second part;

When the imports is 425 metric tons of lemon, we have;

$\overline y$ = -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:

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