This Question 18 pts This Testi 250 pt Find the equation of

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 below

Solution

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