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 (DayPct=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.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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
Pearson
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 (DayPct=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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