find the regression equation, letting the first variable be the predictor (x) variable. using the listed…

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? use a significance level of 0.05.\nlemon imports 232 266 361 465 550\ncrash fatality rate 16 15.8 15.4 15.5 15\n\nfind the equation of the regression line.\n$hat{y}=square+square x$\n(round the y - intercept to three decimal places as needed. round the slope to four decimal places as needed.)

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? use a significance level of 0.05.\nlemon imports 232 266 361 465 550\ncrash fatality rate 16 15.8 15.4 15.5 15\n\nfind the equation of the regression line.\n$hat{y}=square+square x$\n(round the y - intercept to three decimal places as needed. round the slope to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate necessary sums

Let $x$ be lemon - imports and $y$ be crash - fatality rate. $n = 5$ (number of data points). $\sum x=232 + 266+361+465+550 = 1874$ $\sum y=16 + 15.8+15.4+15.5+15 = 77.7$ $\sum x^{2}=232^{2}+266^{2}+361^{2}+465^{2}+550^{2}=232^{2}+70756 + 130321+216225+302500=750028$ $\sum xy=232\times16+266\times15.8+361\times15.4+465\times15.5+550\times15$ $=3712+4202.8+5559.4+7197.5+8250=28921.7$

Step2: Calculate the slope $b_1$

The formula for the slope $b_1$ of the regression line is $b_1=\frac{n\sum xy-\sum x\sum y}{n\sum x^{2}-(\sum x)^{2}}$ $n\sum xy=5\times28921.7 = 144608.5$ $\sum x\sum y=1874\times77.7 = 145619.8$ $n\sum x^{2}=5\times750028=3750140$ $(\sum x)^{2}=1874^{2}=3511876$ $b_1=\frac{144608.5 - 145619.8}{3750140-3511876}=\frac{- 1011.3}{238264}\approx - 0.0042$

Step3: Calculate the y - intercept $b_0$

The formula for the y - intercept $b_0$ is $b_0=\bar{y}-b_1\bar{x}$ $\bar{x}=\frac{\sum x}{n}=\frac{1874}{5}=374.8$ $\bar{y}=\frac{\sum y}{n}=\frac{77.7}{5}=15.54$ $b_0 = 15.54-(-0.0042)\times374.8=15.54 + 1.5742=17.114$

Answer:

$\hat{y}=17.114-0.0042x$