(20 points total) A team of anthropologists and nutrition experts investigated t
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Question
(20 points total) A team of anthropologists and nutrition experts investigated the influence of age (xi) and protein content in diet on height in cm () for children in New Guinea. The protein content is classified as either "rich" or "poor. Define 2 to be l if the protein content is rich, and 0 if it is poor. (5 points) Give the regression model including an interaction between xi and x2. a. (5 points) Estimate the change in mean height, if age is increased by one year, for children with a protein-rich diet. b. ( 10 points) Perform a hypothesis test at 5% significance level to determine if the relationship between age and height is the same for children with protein-rich diets as it is for children with protein-poor diets. Give the hypotheses, test statistic, P-value, and conclusion. c. Predictor Constant X1 X2 XIX2 Coef 51.23 8.69 40.30 12.85 -0.48 633 0.90 137.35 7.32Explanation / Answer
(A)
Based on the table given using the Coef (coefficients of regression),
The regression line is
y = 51.23 + 8.69 * X1 - 0.90 * X2 + 7.32 * X1X2
(B)
x2 = 1 if the protein content is rich
The estimated change in mean height (y)
if age (x1) is increased by 1 year
for children with protein rich diet (x2 = 1)
= 8.69 + 7.32
= 16.01 cm
(c)
H0: The relation between height and age is same for protein rich and protein poor children.
H1: The relation between height and age is not same for protein rich and protein poor children.
This hypothesis is tested by the significance of predictor - X1X2
Using the table given and for the predictor X1X2,
T statistic = 7.35
p-value = 0.000
level of significance = 0.05
p-value < 0.05
So, we reject the null hypothesis
and we conclude that the relationship between height and age is not same for children with protein rich diet and children with protein poor diet.
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