Question

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are bundled in clothes to restrict their movement? Data was collected from parents who brought their babies to New York University Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported ages (in weeks) at which their child was first able to crawl a distance of four feet within one minute. The researchers also recorded the average outdoor temperature (in F) 6 months after the babies? date of birth. The resulting data were grouped by month of birth and all data for babies born on a given month averaged together. If we fit the least-squares line to the 12 data points (one for each month) we obtain the following results from a software package. Notice that the temperature given is taken as the explanatory variable and crawling age as the response variable. Dependent variable is the average crawling age R squared = 49.0% S = 1.319 with 12 ? 2 = 10 degrees of freedom

Variable | Coefficient | S.E. of coefficient

Constant | 35.6781 | 1.318

Temperature | -0.077739 | 0.0251

Construct a 95% confidence interval for the slope for the least squares regression line?

A. (-0.134, -0.022)

B. (0.055, 0.105)

C. (0.024, 0.136)

D. (-0.103, -0.053)

E. (0.053, 0.103)

Answer 1

Here, from the given information,

the slope coefficient for the least square regression line is the estimated coefficient of 'Temperature', say

Given: = -0.077739 and its standard deviation SE () = 0.0251

100 (1-)% Confidence interval for this slope coefficient is given by,

Here, for = 5% and for n-2 = 12-2 = 10 df,

= 2.2281388

Hence, = -0.077739 2.2281388 * 0.0251

= (-0.13367,-0.02181)

Rounding to 3 decimal places, the 95% confidence interval for the slope for the least squares regression line is

A.(-0.134,-0.022)