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. A variables selection method is used to build a regression model. SAS output for the final model is given in photo.  Question: What percentage of the variation in percent body fat remains unexplained, even after introducing weight and abdomen circumference into the model, and then also determine the interpretation of the slope for weight?

We wants to assess the relationship between overall GPA (4.0 scale) and amount of time spent weekly on school work of 50 college students. Simple linear regression model is used and some results for the model is given: a) Is it plausible that the true intercept for the model is 2.0? Why or why not? (hint: using interval for intercept) b) If 2.0 is the real intercept for the model, does it make contextual sense? Explain why it is or why it is not. c) Using the model, calculate the number of hours needed to achieve a GPA of 4.0. Then explain why this estimate number of hours is biased. (hint: think about Y).

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled " The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes and depth D is in meters. The report then says, " The regression equation for this bird is: DD = 2.3 + 0.0021 D. %3D (a) What is the slope of the regression line?. ANSWER minutes per meter. (b) According to the regression line, how long does a typical dive to a depth of 400 meters last? ANSWER minutes.

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled, “The relation of dive duration (DD) to depth (D).” Duration DD is measured in minutes, and depth D is in meters. The report then says, “The regression equation for this bird is DD=2.69+0.0138D. (a) What is the slope of the regression line? (Enter your answer rounded to four decimal places.) slope =     (b) On average, if the depth of the dive increases by one meter, what is the increase in the diving duration? (Enter your answer rounded to four decimal places.) increase in duration =   minutes (c) According to the regression line, how long does a typical dive to a depth of 168 meters last? (Enter your answer rounded to three decimal places.) length…