8. Does When Food Is Eaten Affect Weight Gain?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 =0.740P-Value =0.000--------------------------------------------------------------The regression equation isBMGain=1.11+0.127DayPct 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% (a) What is the correlation between these two variables? What is the p-value from a test of the correlation? (b) What gain is predicted for a mouse that eats 55% of its calories during the day (D⁢a⁢y⁢P⁢c⁢t⁢=55)? Round your answer to two decimal places. (c) What is the estimated slope in this regression model? Round your answer to three decimal places.

Question

8. Does When Food Is Eaten Affect Weight Gain?

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+0.127DayPct

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%

(a) What is the correlation between these two variables? What is the p-value from a test of the correlation?

(b) What gain is predicted for a mouse that eats 55% of its calories during the day (D⁢a⁢y⁢P⁢c⁢t⁢=55)? Round your answer to two decimal places.

(c) What is the estimated slope in this regression model? Round your answer to three decimal places.

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