This Question 18 pts This Testi 250 pt Find the equation of the line for the giv
ID: 3396388 • Letter: T
Question
This Question 18 pts This Testi 250 pt Find the equation of the line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to prodict the value of y for cach of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs shown in the table below 190 (a)x-160 calories (b) x 100 calories (d) x -200 calories 180 120 12070 330 380 (c) x-130 calories Find the regression equation. (Round to three decimal places as needed.) Choose the correct graph below OA. OB. Oc. OD. 200 (a) Predict the value of y for x-160. Choose the correct answer belowExplanation / Answer
Q1.
a.
Mean of X = X / n = 138.3333
Mean of Y = Y / n = 406.6667
(Xi - Mean)^2 = 9883.33
(Yi - Mean)^2 = 51733.33
(Xi-Mean)*(Yi-Mean) = 21966.67
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 21966.67 / 9883.33 = 2.223
bo = Y / n - b1 * X / n
bo = 406.6667 - 2.223*138.3333 = 99.207
Y = bo + b1 X
Y'=99.207+2.223*X
b)
Option D
c)
when x = 160 => 99.207+2.223*(160) =454.887
d)
When x = 100 => 99.207+2.223*(100) =321.507
when x = 100=> 377.454-0.391* (100) = 338.354
Line of Regression Y on X i.e Y = bo + b1 X Xi Yi (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 150 430 136.112 544.443 272.22 180 480 1736.114 5377.773 3055.56 120 330 336.11 5877.783 1405.55 120 380 336.11 711.113 488.89 70 270 4669.44 18677.787 9338.89 190 550 2669.448 20544.435 7405.56