2) Attached to the end is a scatterplot of predicted by residual values for a simple linear regression analysis. Use this plot to comment briefly on the validity of the assumptions of linearity, independence, normality, and homogeneity of variance for this simple linear regression analysis.  3) If you are planning a research study in which x values are predetermined, and then y values are measured in order to perform a simple linear regression analysis, would the standard error of the slope estimate in the model yi = B0 + B1xi + ei be lower by placing the x values relatively close together, or far apart? Briefly explain. (Hint: look at the formula for the standard error of the slope)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 37E
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2) Attached to the end is a scatterplot of predicted by residual values for
a simple linear regression analysis. Use this plot to comment briefly on the validity of the
assumptions of linearity, independence, normality, and homogeneity of variance for this simple
linear regression analysis. 

3) If you are planning a research study in which x values are predetermined, and then y
values are measured in order to perform a simple linear regression analysis, would the standard
error of the slope estimate in the model yi = B0 + B1xi + ei be lower by placing the x values
relatively close together, or far apart? Briefly explain. (Hint: look at the formula for the
standard error of the slope)

e
S
300 ^
200 ^
"
"
"
i
d 100
u
a
"
-100 ^
Residual by predicted plot for a simple linear regression analysis
Plot of res*pred. Legend: A = 1 obs, B = 2 obs, etc.
-100
A A
AB A
AA A A A
-50
A A
B A A AA
AAA A B AA B A
A A A A A
0
A
A A
AAA A
A A AB A A AB
AA
A A A B AA
B
BA A A
AA A A
A
A
100
A A
A AA AA
AA
A
A
Predicted Value of y
A
A
A
A
A
150
A
A
A
Šƒ^ƒ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒ^ƒfƒƒƒƒƒƒƒƒ^ƒƒ
50
A
A
A A
A
A
200
250
Transcribed Image Text:e S 300 ^ 200 ^ " " " i d 100 u a " -100 ^ Residual by predicted plot for a simple linear regression analysis Plot of res*pred. Legend: A = 1 obs, B = 2 obs, etc. -100 A A AB A AA A A A -50 A A B A A AA AAA A B AA B A A A A A A 0 A A A AAA A A A AB A A AB AA A A A B AA B BA A A AA A A A A 100 A A A AA AA AA A A Predicted Value of y A A A A A 150 A A A Šƒ^ƒ¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨ƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒ^ƒfƒƒƒƒƒƒƒƒ^ƒƒ 50 A A A A A A 200 250
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