A pediatrician wants to determine the relation that may exist between a child\'s

Question

A pediatrician wants to determine the relation that may exist between a child's height and head cireumference. She randomly selects 8 chidren, measures their height arnd head circunference, and obtairs the dala shown in the table 17.5 17.2 25.5 26.25 25.5 28 26 a) lf the pediatrician wants lo use height to predict head circumlerence, delermine wich variable is the explanalory variable and which is the response variable O The sxplanatory variable is head cincurnference and the response variable is height O The explanatory vanable is height and the response variable is head cireumference (b) Draw a scatter diagram. Which of the following represents the data? O A O B. O C. D. 16 18. 189 25 Cincm c) Compute the linear comelation coefficient between the height and head circumferance of a child Round to three decimal places as needed)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Head Circumference
Independent Variable: Height
Head Circumference = 11.90847 + 0.2010929 Height
Sample size: 8
R (correlation coefficient) = 0.87798411
R-sq = 0.7708561
Estimate of error standard deviation: 0.10703829

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Option B is correct.

b) Scatter Diagram: Option D is correct.

c) r = 0.878

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 11.90847 1.1895356 0 6 10.011025 <0.0001 Slope 0.2010929 0.044759847 0 6 4.4927074 0.0041

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