Body frame size is determined by a person\'s wrist circumference in relation to
ID: 3375371 • Letter: B
Question
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 80 555 6 05 8.5 Wrist Circumference (in) Coefficients Estimate Std Err t-value value (Intercept 21.6482 6.1123 3.5417 0.00147 wrist7.0025 0.868 8.0676 1.14E-8 Residual standard error: 4.1368 on 27 degrees of freedom R-squared: 0.7068, Adjusted R-squared: 0.6959 F-statistic: 65.0856 on 1 and 27 DF, p-value: 1.14 E -8 Preview 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 e) One of the points on the scatterplot is (6.8,75.7). Calculate the residual for this point. f) The mean wrist circumference for this data is 6.986 inches. Calculate the mean height for this data. g) When predicting heights, what is a "typical" error using this linear model? 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) inches inches inches inchesExplanation / Answer
SolutionA:
Equation of best fir line is
y=21.6482+7.0025x
SolutionB:
correlation coefficient
r=sqrt( r sq)= sqrt(0.7068)
r=0.840714
Intrepretation: there exists a high positive relationship between height and wrist.
As wrist increases height increases
Soluionc:
r sq=coedfficient of determination
r sq=0.7068
Intrepretation:0.7068=0.7068*100=70.68% variation in height is explained by model.Good model
Solutiond:
we have
y=21.6482+7.0025x
height=21.6482+7.0025*wrist
For wrist=6 inches
height=21.6482+7.0025*6
height=63.6632 inches