The and age of each child in a random sample of children was recorded The value of the correlation coefficient between height and the children in the sample was 0.8 . Based on the line created from the data to the height of a child based on age which of the following is a correct statement ?

Options :

A.) On average, the height of a child is 80% of the age of the child.

B.) The least-squares regression line of height versus age will have a slope of 0.8.

C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

D.) The least-squares regression line will correctly predict height based on age 80% of the time.

E.) The least-squares regression line will correctly predict height based on age 64% of the time.

C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

Step-by-step explanation: from the scenario stated above, The correlation Coefficient R = 0.8, which shows the strength of relationship between age and height of children. From the value of correlation Coefficient Given, we can obtain the Coefficient of determination (R²) which gives the percentage of Variation which can be explained by the regression model.

Hence the Coefficient of determination (R²) = 0.8² = 0.64. Hence, the proportion of variation in height of children which can he due to age is 0.64 while 0.36 can be based on other factors.

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