Babies Typically Learn to Crawl Approximately 6 Months After Birth

Multiple Choice

Babies typically learn to crawl approximately 6 months after birth. However, it may take longer for babies to learn to crawl in the winter, when they are often bundled in clothes that restrict their movement. Thus, there may be an association between a baby's crawling age and the average temperature during the month they first try to crawl. Below are the average ages (in weeks) at which babies began to crawl for a sample of babies born in each of the 12 months of the year. In addition, the average temperature (in °F) for the month that is 6 months after the birth month is listed.
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$$\begin{array} { | l | l | l | } \hline \text { Birth month } & \text { Average crawling age } & \text { Average temperature } \\\hline \text { January } & 29.84 & 66 \\\hline \text { February } & 30.52 & 73 \\\hline \text { March } & 29.70 & 72 \\\hline \text { April } & 31.84 & 63 \\\hline \text { May } & 28.58 & 52 \\\hline \text { June } & 31.44 & 39 \\\hline \text { July } & 33.64 & 33 \\\hline \text { August } & 32.82 & 30 \\\hline \text { September } & 33.83 & 33 \\\hline \text { October } & 33.35 & 37 \\\hline \text { November } & 33.38 & 48 \\\hline \text { December } & 32.32 & 57 \\\hline\end{array}$$ We want to investigate whether the average age at which infants begin to crawl (y) can be predicted from the average outdoor temperature (x) 6 months after birth, when the babies are likely to begin crawling. We decide to fit a least-squares regression line to the data, with x as the explanatory variable and y as the response variable. We compute the following quantities:
R = correlation between x and y = -0.7
X?= mean of the values of x = 50.25
?= mean of the values of y = 31.77
S_x = standard deviation of the values of x = 15.85
S_y = standard deviation of the values of y = 1.76
The correlation between the crawling age and height of children is found to be about r = 0.7. Suppose we use the crawling age x of a child to predict the height y of the child from a least-squares regression line. What can we conclude?

A) The least-squares regression line of y on x would have a slope of 0.7.
B) The fraction of the variation in heights explained by the regression line of y on x is 0.49.
C) Approximately 70% of the time, crawling age will accurately predict height.
D) Height is generally 70% of a child's crawling age.