Researchers at a large nutrition and weight management company are trying to build a model to predict a person's body fat percentage from an array of variables such as body weight,height,and body measurements around the neck,chest,abdomen,hips,biceps,etc.A variable selection method is used to build a simple model.SPSS output for the final model is given below. What is a 90% confidence interval for $\beta$₁,the coefficient of weight,based on these results? A)-0.162 ± 0.038 B)-0.162 ± 0.064 C)-0.162 ± 0.525 D)-0.162 ± 4.230

Question

Quizplus · Accepted Answer

The confidence interval for the coefficient of weight (B1) is given by: -0.162 ± t(0.05/2, 321)SE(B1) where t(0.05/2, 321) is the t-value with 321 degrees of freedom at the 0.05/2 significance level (since it is a two-tailed test with alpha=0.10), and SE(B1) is the standard error of B1 from the SPSS output (0.032). Using a t-value calculator or a t-table, we find that t(0.025, 321) is approximately 1.97. Therefore, the 90% confidence interval is: -0.162 ± (1.97)(0.032) = -0.162 ± 0.063 Rounding to three decimal places, we get: -0.162 ± 0.064 So, the best choice is B, which gives the correct confidence interval for F1F1F1S1F1F1F10₁ to 1 decimal place.

Researchers at a Large Nutrition and Weight Management Company Are β\betaβ

Researchers at a Large Nutrition and Weight Management Company Are $\beta$