Question

Heights​ (cm) and weights​ (kg) are measured for 100 randomly selected adult​ males, and range from heights of 134 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbar = 167.46​cm, y overbar = 81.44​kg, r = 0.376​, P- Value = 0.000​, and y with caret = -103+1.07x. Find the best predicted value of y with caret ​(weight) given an adult male who is 150 cm tall. Use a 0.10 significance level.

The best predicted value of y with caret for an adult male who is 150 cm tall is ___kg.

​(Round to two decimal places as​ needed.)

Answer 1

r = 0.376

For finding the best-predicted value of y we have to test the correlation coefficients.

The null and alternative hypothesis is

Level of significance = 0.10

Degrees of freedom = n - 2 = 100 - 2 = 98

Critical value = 0.173 ( using pearson table)

r > critical value we reject null hypothesis.

By using p-value we can also say about the null hypothesis.

P-value = 0.0000 < 0.10 we reject null hypothesis.

If r is significant ( We reject H0), use regression equation is the best predictor.

If r is not significant ( Do not reject H0), we cant use regression equation but we have use \bar{y} as best predictor.

So the regression equation is the best predictor of y.

caret = -103+1.07x.

x = 150

caret = -103+1.07*150 = 57.50

The best-predictedd value of y with caret for an adult male who is 150 cm tall is 57.50kg