Question

A week-long study of weight change, exercise, and caloric intake was conducted among a sample of members at a local gym. The variables are as follows: DV = weight change in pounds during the week IV1 = mean number of hours of aerobic exercise each day IV2 = mean number of calories eaten each day Note that weight change is defined as the difference between one's weight at the beginning of the week and one's weight at the end of the week. A positive value indicates one lost weight at the end of the week (e.g., weight at start = 300, weight at end = 250, difference = 300 - 250 = 50 lbs lost). In the study all participants lost weight, so scores on the DV are all positive. Note that a negative value indicates one would gain weight during the week. Results of the regression analysis follow. Table 8: Regression of Weight Loss on Hours of Exercise and Caloric intake Variable b se b 95% CI Hours of Exercise 0.27 0.11 0.05, 0.49 Caloric Intake -0.002 .0008 -0.0035, -0.0004 Intercept 8.50 0.73 7.05, 9.95 Note: R² = .35, adj. R2 = .35, F = 22.18, df = 2,117; n = 120 Answer the following questions about this regression analysis. (2 point each; 6 points total) (a) Which predictors of weight loss are statistically significant, if either? (b) What is the predicted weight loss for someone who consumes 2,000 calories per day on average and exercises 1 hour per day on average? (c) What is the literal interpretation for the slope of hours of aerobic exercise (b1 = 0.27)?

Answer 1

Ans a ) from the output of regression analysis

both the predictor variable is statistically significant because of the confidence interval contains only positive and negative values and the calculated p-value is less than 0.05.

ans b ) when calorie intake = 2000 and exercise hours is 1 hour

predicted weight loss =8.50 -0.002*2000 +0.27 * 1= 4.77

ans c )

for every hour increase in the aerobic exercise, there is a corresponding 0.27 increase in predicted weight loss