Find the regression equation, letting the first variable be the predictor (x) va

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 525 metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports 226264-366-470-539-o Crash Fatality Rate 16 157 15.4 15.3 15 Find the equation of the regression line (Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.) The best predicted crash fatality rate for a yearin which there are 525 metric tons of lemon imports s fatalities per 100,000 population. Round to one decimal place as needed.) Is the prediction worthwhile? O A. Since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile. B. Since the sample size is small, the prediction 's not appropriate O C. Since there appears to be an outlier, the prediction is not appropriate OD. Since common sense suggests there should not be much of a relationship between the two variables, the prediction does not make much sense. Click to select your answer(s) el

Explanation / Answer

calculation procedure for regression

mean of X = X / n = 370.8

mean of Y = Y / n = 15.48

(Xi - Mean)^2 = 70754.8

(Yi - Mean)^2 = 0.59

(Xi-Mean)*(Yi-Mean) = -196.12

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= -196.12 / 70754.8

= -0.003

bo = Y / n - b1 * X / n

bo = 15.48 - -0.003*370.8 = 16.508

value of regression equation is, Y = bo + b1 X

Y'=16.508-0.003* X

predict when x=525,

Y'=16.508-0.003* 525 = 14.933

Option A

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 226 16 20967.04 0.27 -75.296 264 15.7 11406.24 0.048 -23.496 355 15.4 249.64 0.006 1.264 470 15.3 9840.64 0.032 -17.856 539 15 28291.24 0.23 -80.736

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