Question

Asked Jan 16, 2020

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Lemons and Car Crashes Using the listed lemon/crash data, find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports. Is the prediction worthwhile?

Step 1

**Regression:**

The regression analysis is conducted here by using EXCEL. The software procedure is given below:

- Enter the data.
- Select
**Data > Data Analysis > Regression> OK**. - Enter
**Input Y Range**as**CRASH FERTILITY RATES**. - Enter
**Input X Range**as**LEMON IMPORTS**. - Click
**OK**.

The output using EXCEL is as follows:

Step 2

From the output, regression equation is, *Crash Fatality Rate*= 16.5-0.003(*Lemon Imports*).

*Strategy for Predicting the y value*:

Analyze the below mentioned conditions for predicting the *y* value.

- In scatterplot, the regression line fits the point well.
- The value of
*r*indicates that there is a linear correlation between the variables. - The prediction value is not away from the range of the given sample data.

If the regression equation satisfies the above mentioned conditions, then the regression is said to be a good model. Here, substitute the given value of *x *into the regression equation to predict the value of *y*.

If the regression equation does not satisfy the above conditions, then the regression is not a good model. Here, the best predicted value of *y *is the value of y-bar.

The scatter diagram, along with the best fitted line (least-squares regression line) for the data is as follows:

Step 3

The horizontal axis represents lemon imports and the vertical axis represents crash fertility rates.

From the plot, it is observed that the regression line fit the points well.

*Correlation coefficient r:*

The hypotheses are given below:

*Null hypothesis:*

*H*0: r = 0

That is, there is no linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates.

*Alternative hypothesis:*

*H*a: r≠ 0

That is, there is a linear correlation between the the weights of lemon imports from Mexico and U.S. car fatality rates.

*Sample correlation coefficient:*

The value of the sample correlation coefficient (*r*) can be obtained using Excel formula.

Enter the function, =CORREL(A2:A5,B2:B5).

Thus, the value of the sample correlation coefficient, *r *is –0.959.

**Conclusion:**

The *P*-value is...

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