(а) y 90 54 50 53 80 91 35 41 60 48 35 61 60 71 40 56 60 71 55 68 40 47 65 36 55 53 35 11 50 68 60 70 65 57 90 79 50 79 35 59 A data set consist of dependent variable (y) and independent variable (x) as shown above. It is claims that the relationship between the x and y can be modelled through a regression model as follows: ŷ = a+bx where a and b are the estimated values for a and ß (refer to Appendix). (i) Determine the equation of the regression line to predict the y value from the x value. (ii) If the x value is 75, what is the value of y? (iii) Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of significance.
(а) y 90 54 50 53 80 91 35 41 60 48 35 61 60 71 40 56 60 71 55 68 40 47 65 36 55 53 35 11 50 68 60 70 65 57 90 79 50 79 35 59 A data set consist of dependent variable (y) and independent variable (x) as shown above. It is claims that the relationship between the x and y can be modelled through a regression model as follows: ŷ = a+bx where a and b are the estimated values for a and ß (refer to Appendix). (i) Determine the equation of the regression line to predict the y value from the x value. (ii) If the x value is 75, what is the value of y? (iii) Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of significance.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.CR: Review Exercises
Problem 90CR
Related questions
Question
Transcribed Image Text:y
y
90
54
50
53
80
91
35
41
60
48
35
61
60
71
40
56
60
71
55
68
40
47
65
36
55
53
35
11
50
68
60
70
65
57
90
79
50
79
35
59
A data set consist of dependent variable (y) and independent variable (x) as shown
above. It is claims that the relationship between the x and y can be modelled through a
regression model as follows:
ŷ = a+bx
where a and b are the estimated values for a and ß (refer to Appendix).
(i)
Determine the equation of the regression line to predict the y value from the x
value.
(ii)
If the x value is 75, what is the value of y?
(iii)
Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of
significance.
(iv)
Construct a 95% prediction interval for the y with x=35.
Transcribed Image Text:(b)
Consider a regression line that goes through the origin with the following equation
Y, = Bx, +E,, j =1,2,..,n.
Find the least squares estimator of
B,
B.
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