Question

A sample of four 35-year-old males is asked about the average number of hours per week that he exercises, and is also given a blood cholesterol test. The data is recorded in the order pairs given below, in the form (Hours Exercising, Cholesterol Level):(2.5,230),(3.5,211),(4.6,205),(6,180)Suppose that you know that the correlation coefficient r=−0.98300655251967. Find the coefficient of determination for this sample.r-squared = Which of the following is a correct interpretation of the above value of r2? A. Spending more time exercising will make your muscles go big. B. Spending more time exercising causes cholesterol levels to go down. C. 96.630% of the variance in hours spent exercising is explained by changes in cholesterol levels. D. 96.630% of the variance in cholesterol levels is explained by changes in hours spent exercising.

          A sample of four 35-year-old males is asked about the average number of hours per week that he exercises, and is also given a blood cholesterol test. The data is recorded in the order pairs given below, in the form (Hours Exercising, Cholesterol Level):(2.5,230),(3.5,211),(4.6,205),(6,180)Suppose that you know that the correlation coefficient r=−0.98300655251967.
Find the coefficient of determination for this sample.r-squared = 
Which of the following is a correct interpretation of the above value of r2?
 A. Spending more time exercising will make your muscles go big.
 B. Spending more time exercising causes cholesterol levels to go down.
 C. 96.630% of the variance in hours spent exercising is explained by changes in cholesterol levels.
 D. 96.630% of the variance in cholesterol levels is explained by changes in hours spent exercising.

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Added by Sandra W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

05/06/2023

Step 1

The coefficient of determination is found by squaring the correlation coefficient (r). Given that \( r = -0.98300655251967 \): \[ r^2 = (-0.98300655251967)^2 \] Show more…

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A sample of four 35-year-old males is asked about the average number of hours per week that he exercises, and is also given a blood cholesterol test. The data is recorded in the order pairs given below, in the form (Hours Exercising, Cholesterol Level):(2.5,230),(3.5,211),(4.6,205),(6,180)Suppose that you know that the correlation coefficient r=−0.98300655251967. Find the coefficient of determination for this sample.r-squared = Which of the following is a correct interpretation of the above value of r2? A. Spending more time exercising will make your muscles go big. B. Spending more time exercising causes cholesterol levels to go down. C. 96.630% of the variance in hours spent exercising is explained by changes in cholesterol levels. D. 96.630% of the variance in cholesterol levels is explained by changes in hours spent exercising.

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00:01 So i have my data stored in my list one and list two of my calculator.

00:04 And if i do a little scatter plot of this data between list one and list two and do a zoom number nine, the data kind of looks, and i'm just going to kind of show you what my calculator.

00:17 It looks like there is a negative association, not super strong, but it looks something like that.

00:24 Now part b says to compute the sample correlation coefficient.

00:28 And so i'm going to do a chi -squared test, or excuse me, a linreg t -test between those values.

00:39 And i find that the correlation coefficient comes out to be negative .669.

00:46 That's our r value.

00:48 And so that means there is a negative association as association as hours increase.

00:57 It looks like the ldl decreases, but it is moderately linear.

01:05 So it's not super strong.

01:07 Now on part c, it says to write the equation of the regression line.

01:14 And so we have the regression line being one, the y predicted, which is the ldl, is equivalent to 156 .69.

01:26 And then minus 11 .2, i'm going to call it 40x.

01:33 And so we have for every one hour increase, it looks like there is a decrease of about 11 .2 on the ldl.

01:48 Letter d asks us to predict for three hours per week.

01:54 And so i'm going to go to variables, statistics, eq, and input three in place of that value...

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