Question

# Body frame size is determined by a person's wrist circumference in relation to height. A researcher...

Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals. The data is displayed below. 5 5.5 6 6.5 7 7.5 8 8.5 9 60 65 70 75 80 Wrist Circumference (in) Height (in) Coefficients: Estimate Std Err t-value p-value (Intercept) 33.5375 4.4833 7.4806 4.78 E -8 wrist 5.1405 0.6361 8.0818 1.11 E -8 Residual standard error: 2.9252 on 27 degrees of freedom R-squared: 0.7075, Adjusted R-squared: 0.6967 F-statistic: 65.3151 on 1 and 27 DF, p-value: 1.11 E -8 a) Write the equation of the best-fit line. Use x and y for your variables. b) Calculate the correlation coefficient. c) Identify the coefficient of determination. d) Use the equation of the best-fit line to predict the height of a person with a wrist circumference of 6 inches. inches e) One of the points on the scatterplot is (7,74.3). Calculate the residual for this point. inches f) The mean wrist circumference for this data is 6.997 inches. Calculate the mean height for this data. inches g) When predicting heights, what is a "typical" error using this linear model? inches h) What fraction of variability in heights can be explained using the linear model of height vs wrist circumference? Enter your response as a decimal. i) Calculate the correlation coefficient if the heights are measured in feet. (All heights divided by 12.)

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