Find the equation of the regression line for the given data. Then construct a sc

Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. content (in milligrams) for 6 beef hot dogs are shown in the table below. variables has a 170 I I I 70 (b) x 80 calories (d) x-50 calories 120 120 190 (a) x 180 calories (c) x = 130 calories Find the regression equation. (Round to three decimal places as needed.) Choose the correct graph below. B. O c. A. 200 200 200 200

Explanation / Answer

calculation procedure for regression

mean of X = X / n = 136.6667

mean of Y = Y / n = 400

(Xi - Mean)^2 = 9133.334

(Yi - Mean)^2 = 37200

(Xi-Mean)*(Yi-Mean) = 17900

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

= 17900 / 9133.334

= 1.96

bo = Y / n - b1 * X / n

bo = 400 - 1.96*136.6667 = 132.153

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

Y'=132.153+1.96* X

a.

when x = 180 calories then

Y'=132.153+1.96* X

Y' = 132.153 +(1.96*180) =484.953

b.

x= 80 calories

Y' = 132.153 +(1.96*80) =288.953

c.

x =130 calories

Y' =132.153 +(1.96*130) =386.953

d.

x= 50 calories

Y' =132.153 +(1.96*50)=230.153

graph shown

option:A

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 150 410 177.777 100 133.333 170 460 1111.109 3600 1999.998 120 340 277.779 3600 1000.002 120 370 277.779 900 500.001 70 290 4444.449 12100 7333.337 190 530 2844.441 16900 6933.329

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