Height and Weight Last Fall, as Our First Example of Correlation

question 32

Essay

Height and weight Last fall, as our first example of correlation, we looked at the heights and weights of some AP* Statistics students. Here are the scatterplot, the residuals plot, a histogram of the residuals, and the regression analysis for the data we collected from the males. Use this information to analyze the association between heights and weights of teenage boys.

Dependent variable is:WT(lb)
$\mathrm{R}$ squared $=56.6 \%$
$s=14.16 \text { with } 25-2=23$

$\begin{array}{lllll}\text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Const } & -364.403 & 94.61 & -3.85 & 0.0008 \\ \text { HT(in) } & 7.29993 & 1.333 & 5.48 & \leq 0.0001\end{array}$


a. Is there an association? Write appropriate hypotheses. b. Are the assumptions for regression satisfied? Explain. c. What do you conclude?
d. Create a 95% confidence interval for the true slope.
e. Explain in context what your interval means.

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Definitions:

Infertility

The inability of a person to conceive a child naturally after one year of regular, unprotected sexual intercourse.

Conceive

Conceive means to form or devise a plan or idea in the mind.

One Year

A period of time that consists of 12 consecutive months.

Metabolism Decreases

The process by which the body’s ability to convert food and drink into energy slows down, typically as part of aging.