Suppose a doctor measures the height, x, and head circumference, y, of 8 childre

Question

Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is

0.7960.796

and the least squares regression line is

ModifyingAbove y with caret equals 0.182 x plus 12.372y=0.182x+12.372.

Complete parts (a) and (b) below

Height_x   Head Circumference_y

27.75   17.2
25.75   17.0
26.00   17.1
25.00   16.9
27.50   17.6
26.50   17.1
25.75   17.1
26.75   17.3

(a) Compute the coefficient of determination,

Rsquared2.

Rsquared2equals=nothing%

(Round to one decimal place as needed.)

(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

A.

Rsquared2

of the variation in head circumference is not explained by the least-squares regression equation. The linear model appears to be appropriate.

B.

Rsquared2

of the variation in head circumference is explained by the least-squares regression equation. The linear model appears to be appropriate.

C.

Rsquared2

of the variation in head circumference is not explained by the least-squares regression equation. The linear model appears to be not appropriate.

D.

Rsquared2

of the variation in head circumference is explained by the least-squares regression equation. The linear model appears to be not appropriate

Explanation / Answer

Result:

Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is

0.796

and the least squares regression line is

ModifyingAbove y with caret equals 0.182 x plus 12.372y=0.182x+12.372.

Complete parts (a) and (b) below

Height_x   Head Circumference_y

27.75   17.2
25.75   17.0
26.00   17.1
25.00   16.9
27.50   17.6
26.50   17.1
25.75   17.1
26.75   17.3

(a) Compute the coefficient of determination,Rsquared2.

Rsquared2   = 63.36%

(Round to one decimal place as needed.)

R squared = r*r=0.796*0.796

=0.6336

(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.

A.Rsquared2 of the variation in head circumference is not explained by the least-squares regression equation. The linear model appears to be appropriate.

Answer: B.Rsquared2 of the variation in head circumference is explained by the least-squares regression equation. The linear model appears to be appropriate.

C.Rsquared2 of the variation in head circumference is not explained by the least-squares regression equation. The linear model appears to be not appropriate.

D.Rsquared2 of the variation in head circumference is explained by the least-squares regression equation. The linear model appears to be not appropriate

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