Question

Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 191 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield 3 = 167.96 cm, y=81.63 kg, -0.218, P-value = 0.029, and ỹ = - 103 + 1.14x. Find the best predicted value ofŷ (weight) given an adult male who is 159 cm tall. Use a 0.10 significance level. The best predicted value of ý for an adult male who is 159 cm tall is kg. (Round to two decimal places as needed.) Enter your answer in the answer box.

Answer 1

H0 : There is no correlation exists between the variable weight and height.

Ha : There is correlation exists between the variable weight and height.

We are given r = 0.218, so | r | = 0.218 and n = 100

For two tail area ,α = 0.05

n a = 50 60 80 2-tailed testing 2.1 a = .05 a = .01 0.235 0.279 0.361 0.214 0.254 0.330 0.185 0.220 0.286 0.165 0.197 0.256 * 100

Therefore critical value is 0.165

As | r | is greater than 0.165, we reject the null hypothesis H0

So we can conclude that there is significant correlation exists between the variable weight and height.

Therefore we can use the given equation of regression line for prediction.

We are given height x = 159 cm and asked to predict weight y

$\hat{y}$ = -103 + 1.14 x

= -103 + (1.14*159)

$\hat{y}$ = 78.26 kg