2. Thighs and Biceps The quadriceps muscles are the muscles on the front of the

Question

2. Thighs and Biceps The quadriceps muscles are the muscles on the front of the thigh. The equivalent muscles in the front of the upper arms are the biceps. A group of researchers are inter- ested in estimating thigh circumferences based on biceps circumferences. Data were collected on 150 individuals. The data was collected in centimeters and can be found in Thighsvsbiceps.jmp (a) Identify the Explanatory and Response Variables. Make sure you use exact wording from problem statement. i. Explanatory (x): ii. Response (v): (b) Create a scatterplot in JMP through the commands Analyze- >Fit Y by X, and correctly selecting the variables into "X" and "Y". Now fit a least squares regression model to the data (in JMP) by selecting Fit Line from the "red triangle" menu on your scatterplot win dow. Use the scatter plot and output to calculate the value of the correlation coefficient r (report to four decimal places) (c) Now based on the scatter plot and output from part b), describe the relationship between r and y. Make sure to comment on the overall form, strength, direction and possible outliers i. Overall form: Linear or Non-Linear (Choose one) ii. Strength : Strong or Moderate or Weak (Choose one) iii. Direction: Positive or Negative (Choose one) iv. How many outliers are present? (Enter the appropriate digit only) (d) Report the slope of the fitted least squares regression line (to four decimal places)

Explanation / Answer

(a) Explanatory variable : Biceps circumference

Response variable : Thigh Circumference

(b) value of correlation coefficient r = sqrt(R square) = sqrrt (0.6683) = 0.8175

(c) (i) Overall form : Linear

(ii) Strength : Strong (as value of r is high)

(iii) Direction : Positive

(iv) How many outliers are present = One

(d) Slope of the least regression equation b = 1.433402

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