Question

Heights (in centimeters) and weights (in kilograms) of 7 supermodels are given below.

Height (x) 172 176 176 178 176 166 172  

Weight (y) 52 56 55 57 54 47 53

(Note: Compute values to three decimal places of accuracy.)

The regression equation is y= ?_____ .

Regardless of what answer you actually got, suppose your regression equation were

y= -80 + 0.8 x.

This line predicts the weight of a supermodel who is 177 cm tall to be ?___ kg.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -84.344828 + 0.79310345 x
Sample size: 7
R (correlation coefficient) = 0.9755635
R-sq = 0.95172414
Estimate of error standard deviation: 0.79654426

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-84.344828	13.880082	≠ 0	5	-6.0766808	0.0017
Slope	0.79310345	0.07988299	≠ 0	5	9.9283145	0.0002

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	62.541872	62.541872	98.571429	0.0002
Error	5	3.1724138	0.63448276
Total	6	65.714286

Hence,

Regression equation will be:

y = -84.345 + 0.793x

Given regression equation: y = -80 + 0.8x

So for x = 177,

y = -80 + 0.8*177 = 61.6 kg