The authors of the paper"Weight-BearingActivitiyduring Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake" (Journal of Bone and Mineral Research)studied a number of variables they thought might be related to bone mineral density (BMD). One particular variable they thought might be a good predictor of BMD was the Weight of a subject at age 13. The data below provides measurements on 15 subjects involved in this study including their Weight at age 13 and their BMD at age 27.

Weight (kg). BMD

54.4 1.02

59.3 1.26

74.6 1.3

62.0 1.06

73.7 1.44

70.8 1.35.

66.8 1.16

66.7 1.35

64.7 1.22

71.8 1.25

69.7 1.28

64.7 1.17

62.1 1.12

68.5 1.24

58.3 1.01

Which is our dependent/response/outcome variable, in other words, which variable are we trying to predict/explain?

Which is our independent/explanatory/predictor variable, in other words, which variable are we using in order to predict?

In Regression we have a special place for the letters Y and X.

In this data which is our Y variable?

In this data which is our X variable?

You may use Microsoft Excel or Google Sheets to answer the quantitative questions here. Copy and paste data into and adjust if necessary.

What is the Pearson's Correlation Coefficient, r, between Weight and BMD? (round to three decimal places)

Is the relationship between Weight and BMD positive or negative or null?

What is the y-intercept for the Simple Linear Regression line, bo? (round to three decimal places)

What is the slope for the Simple Linear Regression line, b1? (round to three decimal places)

If I have a subject who's Weight at age 13 is 65.3 kg what is her expected or predicted BMD at age 27? (round to two decimal places)