To find the regression equation, we need to determine the slope ($b_1$) and the y-intercept ($b_0$) using the least squares regression formula:

$y = b_0 + b_1x$

where:

• $x$ represents the lemon imports,
• $y$ represents the crash fatality rate.

Step 1: Calculate the necessary sums.

Let’s break down the formulas:

• The slope $b_1$ is given by:

$b_1 = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$

• The y-intercept $b_0$ is given by:

$b_0 = \frac{\sum y}{n} - b_1 \cdot \frac{\sum x}{n}$

Now, compute the following for the data given:

Lemon Imports ($x$)	Crash Fatality Rate ($y$)
234	16
260	15.9
363	15.6
494	15.4
539	15.1

We need:

1. $\sum x$ = sum of lemon imports
2. $\sum y$ = sum of crash fatality rates
3. $\sum x^2$ = sum of squares of lemon imports
4. $\sum xy$ = sum of the product of lemon imports and crash fatality rates
5. $n = 5$ (the number of data points)

Let's calculate these next.We have the following values:

• $\sum x = 1890$
• $\sum y = 78.0$
• $\sum x^2 = 788682$
• $\sum xy = 29287.3$
• $n = 5$

Step 2: Calculate the slope $b_1$

$b_1 = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$ Let's compute the slope $b_1$.The slope of the regression line is approximately $b_1 = -0.0026$ (rounded to four decimal places).

Step 3: Calculate the y-intercept $b_0$

The formula for the y-intercept is:

$b_0 = \frac{\sum y}{n} - b_1 \cdot \frac{\sum x}{n}$

Now, let's compute the y-intercept $b_0$.The y-intercept of the regression line is approximately $b_0 = 16.601$ (rounded to three decimal places).

Step 4: Write the regression equation

The regression equation is:

$\hat{y} = 16.601 - 0.0026x$

Step 5: Prediction for 450 metric tons of lemon imports

To predict the crash fatality rate for $x = 450$ metric tons, substitute $x = 450$ into the regression equation:

$\hat{y} = 16.601 - 0.0026 \times 450$

Let's calculate that next.