Exercise 7.24

7.24 Nutrition at Starbucks, Part I. The scatterplot below shows the relationship between the number of calories and amount of carbohydrates (in grams) Starbucks food menu items contain. 21 Since Starbucks only lists the number of calories on the display items, we are interested in predicting the amount of carbs a menu item has based on its calorie content.

(a) Describe the relationship between number of calories and amount of carbohydrates (in grams)

that Starbucks food menu items contain.

It is a Straight band relationship of curved trend with positive relationship. If amount of calories increase, the carbohydrates will be increased proportionly.

(b) In this scenario, what are the explanatory and response variables?

In this case, the calories is in a relationship to explain or to predict changes in the values of carbohydrates, so the explanatory variable is Calories at x axis, and response variable is Carbohydrates at y axis.

(c) Why might we want to fit a regression line to these data?

We might be interested in predicting the number of carbohydrates in a particular food item based on the number of calories.

We can set up the equation to predict amount of carbohydrates based on particular food item of caories. This method can estimate the uncertainty in the slope and y-intercept for a regression line.

(d) Do these data meet the conditions required for fitting a least squares line?

Linearity: The data are shown in linear, but the variability of the data around the line increases with larger values of x.

Nearly normal residuals: The residuals distribution appears nearly normal.

Constant variability: It is not a constant variability, because the variability of thedata around the line increases with larger values of x. The variability of points around the least square line must remain roughly constant.

Independent observations: The menu item is presumably independent observation, but just involve starbucks only.

It does not satisfy the conditions of linerity and constant variability, so it not fit a least squares line.