# Refer to Example 11 on winning Olympic high jumps. The prediction equation relating

__QUESTION:__

Refer to Example 11 on winning Olympic high jumps. The prediction equation relating y = winning height (in meters) as a function of x_{1} = number of years since 1928 and x_{2} = gender (1 = male, 0 = female) is ŷ = 1.63 + 0.0057x_{1} + 0.348x_{2}.

a. Using this equation, find the prediction equations relating to winning height to year, separately for males and for females.

b. Find the predicted winning height in 2012 for (i) Females, (ii) Males, and show how the difference between them relates to a parameter estimate for the model.

__ANSWER:__

a. Males: ŷ = 1.63 + 0.0057 x1 + 0.348(1) = 1.978 + 0.0057 x1 Females: ŷ = 1.63 + 0.0057 x_{1} + 0.348(0) = 1.63 + 0.0057 x_{1}

b. 2012 – 1928 = 84

(i) Females = 1.63 + 0.0057(84) = 2.11;

(ii) Males = 1.978 + 0.0057(84) = 2.46;

The difference between them is 2.46 – 2.11 = 0.35, the slope for the indicator variable of gender.

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