Consider a set of data (x,y), i = 1, 2, ..., n and the simple linear regression model given by: Y₁ = Bo + B₁x₁ + εi with E(&) = 0, Var(e) = o² and all &'s are independent and normally distributed. Suppose further that a random sample of size 10 is selected and the fitted regression equation is obtained: with b) SB₁ = 0.071 and SSxx = 1568.625. a) If we were to draw a scatter plot for the data, what kind of relationship would be expected? Justify your answer. Construct analysis of variance (ANOVA) and use it to test at 5% level whether or not there is a significant relationship between x and y. Verify the results in b) using a 95% confidence interval. c) ŷ₁2.106 0.933x,
Consider a set of data (x,y), i = 1, 2, ..., n and the simple linear regression model given by: Y₁ = Bo + B₁x₁ + εi with E(&) = 0, Var(e) = o² and all &'s are independent and normally distributed. Suppose further that a random sample of size 10 is selected and the fitted regression equation is obtained: with b) SB₁ = 0.071 and SSxx = 1568.625. a) If we were to draw a scatter plot for the data, what kind of relationship would be expected? Justify your answer. Construct analysis of variance (ANOVA) and use it to test at 5% level whether or not there is a significant relationship between x and y. Verify the results in b) using a 95% confidence interval. c) ŷ₁2.106 0.933x,
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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Question
![Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:
Yi Bo + B₁x₁ + εi
with E() = 0, Var(ɛ;) = o² and all &;'s are independent and normally distributed.
Suppose further that a random sample of size 10 is selected and the fitted regression equation is
obtained:
with SB₁
b)
= 0.071 and SSxx = 1568.625.
a)
If we were to draw a scatter plot for the data, what kind of relationship would be expected?
Justify your answer.
Construct analysis of variance (ANOVA) and use it to test at 5% level whether or not there is
a significant relationship between x and y.
Verify the results in b) using a 95% confidence interval.
c)
ŷi = 2.106 -0.933x₁](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c17a710-26d7-4116-b1b9-95b1f447e8a0%2F4239bb75-90b5-4c0f-a2fc-7beb63366265%2Fs6hec3s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:
Yi Bo + B₁x₁ + εi
with E() = 0, Var(ɛ;) = o² and all &;'s are independent and normally distributed.
Suppose further that a random sample of size 10 is selected and the fitted regression equation is
obtained:
with SB₁
b)
= 0.071 and SSxx = 1568.625.
a)
If we were to draw a scatter plot for the data, what kind of relationship would be expected?
Justify your answer.
Construct analysis of variance (ANOVA) and use it to test at 5% level whether or not there is
a significant relationship between x and y.
Verify the results in b) using a 95% confidence interval.
c)
ŷi = 2.106 -0.933x₁
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