11.21 Consider the following pairs of measurements. D L11021 x y 54 5 4 33 3 -1 2 7 3 0 1 8 65 5 43 3 a. Construct a scatterplot of these data. b. What does the scatterplot suggest about the relation- ship between x and y? xx c. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286, and 3.7143, calculate the least squares estimates of Bo and B. 020; .918 d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain. e. Interpret the y-intercept and slope of the least squares line. Over what range of x are these interpretations meaningful?
11.21 Consider the following pairs of measurements. D L11021 x y 54 5 4 33 3 -1 2 7 3 0 1 8 65 5 43 3 a. Construct a scatterplot of these data. b. What does the scatterplot suggest about the relation- ship between x and y? xx c. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286, and 3.7143, calculate the least squares estimates of Bo and B. 020; .918 d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain. e. Interpret the y-intercept and slope of the least squares line. Over what range of x are these interpretations meaningful?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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
Transcribed Image Text:11.21 Consider the following pairs of measurements.
D
L11021
x
y
54
5
4
33
3
-1
2
7
3
0
1
8
65
5
43
3
a. Construct a scatterplot of these data.
b. What does the scatterplot suggest about the relation-
ship between x and y?
xx
c. Given that SS = 43.4286, SSxy = 39.8571, y = 3.4286,
and 3.7143, calculate the least squares estimates of
Bo and B. 020; .918
d. Plot the least squares line on your scatterplot. Does the
line appear to fit the data well? Explain.
e. Interpret the y-intercept and slope of the least squares
line. Over what range of x are these interpretations
meaningful?
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