Answer :
The regression line equation for predicting height from shoulder girth is: y = 0.67x + 110.67, where y is the height and x is the shoulder girth.
The regression line equation for predicting height from shoulder girth is: y = 0.67x + 110.67, where y is the height and x is the shoulder girth. The equation is used to predict the height of an individual based on their shoulder girth. The intercept (110.67 cm) indicates the height when the shoulder girth is 0 cm, and the slope (0.67) indicates the increase in height for every 1 cm increase in shoulder girth. This equation can be used to predict the height of an individual given their shoulder girth and to determine how much of a difference in height is associated with a given difference in shoulder girth.
Step 1: Calculate the slope (m) using the correlation coefficient (r): m = r*(SDy/SDx), where SDy is the standard deviation of the height, and SDx is the standard deviation of the shoulder girth.
m = 0.67*(9.41/10.37) = 0.645
Step 2: Calculate the intercept (b) using the mean values of the two variables: b = y - mx, where y is the mean height and x is the mean shoulder girth.
b = 171.14 - 0.645*107.20 = 110.67
Step 3: Substitute the values of the slope (m) and intercept (b) into the regression equation: y = mx + b.
y = 0.645x + 110.67
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