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A study was introduced that examined the effect of light at night on weight gain in mice. In the full study of 27 mice over a four-week period, the mice who had a light on at night gained significantly more weight than the mice with darkness at night, despite eating the same number of calories and exercising the same amount. Researchers noticed that the mice with light at night ate a greater percentage of their calories during the day (when mice are supposed to be sleeping). The computer output shown below allows us to examine the relationship between percent of calories eaten during the day, DayPct, and body mass gain in grams, BMGain. A scatterplot with regression line is also shown below. Pearson correlation of BMGain and DayPct 0.740 P-Value = 0.000 The regression equation is BMGain 1.11 +0.127 DayPct Predictor Coef SE Coef T P Constant 1.113 1.382 0.81 0.428 DayPct 0.12727 0.02315 5.50 0.000 S2.23097 R-Sq - 54.7% R - Sq (adj) = 52.9% O Yes O No The correlation is i The p-value is i 18 16 14 12 (a) Use the scatterplot to determine: Are the conditions reasonably met for using a linear model with this data? What is the conclusion of the test? 6 4 Ho- 20 30 40 50 60 DayPct (b) What is the correlation between these two variables? What is the p-value from a test of the correlation? 70 80 90

A study was introduced that examined the effect of light at night on weight gain in mice. In the full study of 27 mice over a four-week period, the mice who had a light on at night gained significantly more weight than the mice with darkness at night, despite eating the same number of calories and exercising the same amount. Researchers noticed that the mice with light at night ate a greater percentage of their calories during the day (when mice are supposed to be sleeping). The computer output shown below allows us to examine the relationship between percent of calories eaten during the day, DayPct, and body mass gain in grams, BMGain. A scatterplot with regression line is also shown below. Pearson correlation of BMGain and DayPct 0.740 P-Value = 0.000 The regression equation is BMGain 1.11 +0.127 DayPct Predictor Coef SE Coef T P Constant 1.113 1.382 0.81 0.428 DayPct 0.12727 0.02315 5.50 0.000 S2.23097 R-Sq - 54.7% R - Sq (adj) = 52.9% O Yes O No The correlation is i The p-value is i 18 16 14 12 (a) Use the scatterplot to determine: Are the conditions reasonably met for using a linear model with this data? What is the conclusion of the test? 6 4 Ho- 20 30 40 50 60 DayPct (b) What is the correlation between these two variables? What is the p-value from a test of the correlation? 70 80 90

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A study was introduced that examined the effect of light at night on weight gain in mice. In the full study of 27 mice over a four-week period, the mice who had a light on at night gained significantly more weight than the mice with darkness at night, despite eating the same number of calories and exercising the same amount. Researchers noticed that the mice with light at night ate a greater percentage of their calories during the day (when mice are supposed to be sleeping). The computer output shown below allows us to examine the relationship between percent of calories eaten during the day, DayPct, and body mass gain in grams, BMGain. A scatterplot with regression line is also shown below. Pearson correlation of BMGain and DayPct = 0.740 P-Value = 0.000 The regression equation is BMGain = 1.11 +0.127 DayPct Predictor Coef SE Coef T P Constant 1.113 1.382 0.81 0.428 DayPct 0.12727 0.02315 5.50 0.000 S = 2.23097 R - Sq = 54.7% R - Sq (adj) = 52.9% O Yes O No The correlation is i (a) Use the scatterplot to determine: Are the conditions reasonably met for using a linear model with this data? The p-value is i 18 16 14 12 What is the conclusion of the test? 10 8 6 4 2 ✓ Ho. 20 30 40 (b) What is the correlation between these two variables? What is the p-value from a test of the correlation? 50 60 DayPct 70 80 90
Transcribed Image Text:A study was introduced that examined the effect of light at night on weight gain in mice. In the full study of 27 mice over a four-week period, the mice who had a light on at night gained significantly more weight than the mice with darkness at night, despite eating the same number of calories and exercising the same amount. Researchers noticed that the mice with light at night ate a greater percentage of their calories during the day (when mice are supposed to be sleeping). The computer output shown below allows us to examine the relationship between percent of calories eaten during the day, DayPct, and body mass gain in grams, BMGain. A scatterplot with regression line is also shown below. Pearson correlation of BMGain and DayPct = 0.740 P-Value = 0.000 The regression equation is BMGain = 1.11 +0.127 DayPct Predictor Coef SE Coef T P Constant 1.113 1.382 0.81 0.428 DayPct 0.12727 0.02315 5.50 0.000 S = 2.23097 R - Sq = 54.7% R - Sq (adj) = 52.9% O Yes O No The correlation is i (a) Use the scatterplot to determine: Are the conditions reasonably met for using a linear model with this data? The p-value is i 18 16 14 12 What is the conclusion of the test? 10 8 6 4 2 ✓ Ho. 20 30 40 (b) What is the correlation between these two variables? What is the p-value from a test of the correlation? 50 60 DayPct 70 80 90
(c) What gain is predicted for a mouse that eats 54% of its calories during the day (Day Pct = 54)? Round your answer to two decimal places. BMGain = (d) What is the estimated slope in this regression model? Round your answer to three decimal places. b₁ = Interpret the slope in context. (e) What is the p-value for a test of the slope? The p-value is i What is the conclusion of the test? Ho. (f) What is the relationship between the p-value of the correlation test and the p-value of the slope test? O They are the same. O They are different. (g) What is R²? R² = grams Interpret it in context. %
Transcribed Image Text:(c) What gain is predicted for a mouse that eats 54% of its calories during the day (Day Pct = 54)? Round your answer to two decimal places. BMGain = (d) What is the estimated slope in this regression model? Round your answer to three decimal places. b₁ = Interpret the slope in context. (e) What is the p-value for a test of the slope? The p-value is i What is the conclusion of the test? Ho. (f) What is the relationship between the p-value of the correlation test and the p-value of the slope test? O They are the same. O They are different. (g) What is R²? R² = grams Interpret it in context. %
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