Question

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is y-hat = -181.342 + 144.46x and the standard error of estimate is se=5.0015. Find the 95% prediction interval for the weight of a person whose height is 1.75 m.

x height (meters) y weight (kg)

1.61 54

1.72 62

1.78 70

1.80 84

1.67 61

1.88 92

Answer 1

= (1.61 + 1.72 + 1.78 + 1.80 + 1.67 + 1.88) / 6 = 1.743333

= (1.61 - 1.743333)² +  (1.72 - 1.743333)² +  (1.78- 1.743333)² +  (1.80- 1.743333)² +  (1.67- 1.743333)² +  (1.88- 1.743333)²

= 0.04693333

yp = -181.342 + 144.46 * 1.75 = 71.463

Degree of freedom , df = n-2 = 6 - 2 = 4

t value of 95% prediction interval and df = 4 is 2.78

95% prediction interval for the weight of a person whose height is 1.75 is

yp t * se *

= 71.463 2.78 * 5.0015 *

= 71.463 2.78 * 5.0015 * 1.080562

= 71.463   15.02432

= (71.463 - 15.02432, 71.463 + 15.02432)

= (56.43868, 86.48732)