Question

The following data were collected during a study of consumer buying patterns:

Observation	x	y	Observation	x	y
1	20	78	8	23	81
2	27	84	9	10	69
3	43	79	10	13	68
4	29	80	11	21	85
5	53	98	12	28	91
6	44	97	13	34	93
7	33	82

b. Obtain a linear regression line for the data.(Round your intermediate calculations and final answers to 3 decimal places.)

y =  +  x

c. What percentage of the variation is explained by the regression line? (Do not round intermediate calculations. Round your answer to the nearest whole percent. Omit the "%" sign in your response.)

Approximately  % of the variation in the dependent variable is explained by the independent variable.

d. Use the equation determined in part b to predict the expected value of y for x = 47. (Round your intermediate calculations and final answers to 3 decimal places.)

y =

Answer 1

From our calculation, Sum(X) = 378, Sum(Y) = 1085, Sum(X*Y) = 32645, Sum(X^2) = 12832, Yavg = 83.4615,Xavg = 29.0769

We know m= (N*Sum(X*Y) - Sum(X)*Sum(Y))/(N*Sum(X^2) - (Sum(X))^2) = (13*32645 - 378*1085)/(13*12832 - (378)^2) = 0.5956

b = Yavg - m*Xavg = 83.4615 - 0.5956*29.0769 = 66.1433

Therefore our regression equation in terms of Y = B + m*X is Y = 66.1433 + 0.5956*X

From our calculation, Sum((Y - Yavg)^2) = 1063.2307, Sum((Ypredicted - Yavg)^2) = 653.0478

R² = Sum((Ypredicted - Yavg)^2)/Sum((Y - Yavg)^2) = 653.0478/1063.2307 = 0.6142

Therefore the model explains 61.42% of variation.

At X = 47, Y = 66.1433 + 0.5956*47 = 94.1365

The calculation done in excel is as follows-

Please Like & Provide your reviews in comments. :-)