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Body measurements, Part II. The scatterplot below shows the relationship between weight measured in kilograms and hip girth measured in centimeters from the data described in Exercise 8,13 . (a) Describe the relationship between hip girth and weight. (b) How would the relationship change if weight was measured in pounds while the units for hip girth remained in centimeters?

Over-under, Part II. Suppose we fit a regression line to predict the number of incidents of skin cancer per 1,000 people from the number of sunny days in a year. For a particular year, we predict the incidence of skin cancer to be 1.5 per 1,000 people, and the residual for this year is \(0.5 .\) Did we over or under estimate the incidence of skin cancer? Explain your reasoning.

Body measurements, Part III. Exercise 8.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is \(107.20 \mathrm{~cm}\) with a standard deviation of \(10.37 \mathrm{~cm}\). The mean height is \(171.14 \mathrm{~cm}\) with a standard deviation of \(9.41 \mathrm{~cm} .\) The correlation between height and shoulder girth is 0.67 (a) Write the equation of the regression line for predicting height. (b) Interpret the slope and the intercept in this context. (c) Calculate \(R^{2}\) of the regression line for predicting height from shoulder girth, and interpret it in the context of the application. (d) A randomly selected student from your class has a shoulder girth of \(100 \mathrm{~cm}\). Predict the height of this student using the model. (e) The student from part (d) is \(160 \mathrm{~cm}\) tall. Calculate the residual, and explain what this residual means. (f) A one year old has a shoulder girth of \(56 \mathrm{~cm}\). Would it be appropriate to use this linear model to predict the height of this child?

Body measurements, Part IV. The scatterplot and least squares summary below show the relationship between weight measured in kilograms and height measured in centimeters of 507 physically active individuals. (a) Describe the relationship between height and weight. (b) Write the equation of the regression line. Interpret the slope and intercept in context. (c) Do the data provide strong evidence that an increase in height is associated with an increase in weight? State the null and alternative hypotheses, report the p-value, and state your conclusion. (d) The correlation coefficient for height and weight is \(0.72 .\) Calculate \(R^{2}\) and interpret it in context.