4. If appropriate, estimate the weight for someone who gets 6.5 hours of sleep per night. Interpret the estimate. 5. If appropriate, estimate the weight for someone who gets 1 hour of sleep per night. Interpret the estimate

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
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Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question 4,5 and 6
Consider the following scenario to answer the questions below:
Researchers would like to determine, for adults, if there is a linear relationship between number of
hours of sleep obtained per night and weight (in pounds). If so, the researchers would like a model that
will estimate the weight of adults given the number of hours of sleep obtained per night. To answer the
questions, the following data was obtained:
Chapte Weight
Hours of Sleep
Weight
Hours of Sleep
143
5.25
109
8.75
Sen
135
6.55
131
7
140
4
109
122
6.3
122
7.75
121
7.15
112
8.75
122
7
133
7.2
130
5
115
8.
The 138
4.35
112
9.
W146
3.5
120
8.5
121
8.11
106
9.25
1. Is this a Simple, Multiple, or Multivariate model? Explain.
2. What are the dependent and independent variables?
3. Is the relationship between the variables linear?
4. If appropriate, estimate the weight for someone who gets 6.5 hours of sleep per night. Interpret the
estimate.
5. If appropriate, estimate the weight for someone who gets 1 hour of sleep per night. Interpret the
estimate
6. Find and interpret a 95% confidence interval for how the average weight changes for a one hour
increase in sleep per night.
7. Find and interpret a 95% confidence interval for the average weight given 6.5 hours of sleep per
night is obtained.
8. Find and interpret a 95% prediction interval for the weight of a person who gets 6.5 hours of sleep
per night.
9. Find and interpret the correlation coefficient.
10. Find and interpret the coefficient of determination.
Transcribed Image Text:Consider the following scenario to answer the questions below: Researchers would like to determine, for adults, if there is a linear relationship between number of hours of sleep obtained per night and weight (in pounds). If so, the researchers would like a model that will estimate the weight of adults given the number of hours of sleep obtained per night. To answer the questions, the following data was obtained: Chapte Weight Hours of Sleep Weight Hours of Sleep 143 5.25 109 8.75 Sen 135 6.55 131 7 140 4 109 122 6.3 122 7.75 121 7.15 112 8.75 122 7 133 7.2 130 5 115 8. The 138 4.35 112 9. W146 3.5 120 8.5 121 8.11 106 9.25 1. Is this a Simple, Multiple, or Multivariate model? Explain. 2. What are the dependent and independent variables? 3. Is the relationship between the variables linear? 4. If appropriate, estimate the weight for someone who gets 6.5 hours of sleep per night. Interpret the estimate. 5. If appropriate, estimate the weight for someone who gets 1 hour of sleep per night. Interpret the estimate 6. Find and interpret a 95% confidence interval for how the average weight changes for a one hour increase in sleep per night. 7. Find and interpret a 95% confidence interval for the average weight given 6.5 hours of sleep per night is obtained. 8. Find and interpret a 95% prediction interval for the weight of a person who gets 6.5 hours of sleep per night. 9. Find and interpret the correlation coefficient. 10. Find and interpret the coefficient of determination.
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