Linear Regression Practice 4:
1. The least-squares regression line is
a. the line that passes through the most data points.
b. the line that makes the sum of the squares of the vertical distances of the data points from the line
(the sum of squared residuals) as small as possible.
c. the line such that half of the data points fall above the line and half fall below the line.
d. all of the above.
The following is a scatter plot of the liters of alcohol from drinking wine per person and the death rates from heart disease per 100,000 people for each of 9 countries. The least-squares regression line has been drawn in on the plot.
2. Based on the least-squares regression line we would predict that in a country where, per person, 7 liters of alcohol from wine is consumed, the death rate from heart disease per 100,000 people would be about
a. 50.
b. 100.
c. 260.
d. 700.
Use the following information to answer questions 3-5.
Babies typically learn to crawl approximately six months after birth. 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.
In a study, for each month of the year, researchers sampled babies born during that month and measured the average age (in weeks) of first crawl. They also recorded the average temperature 6 months later (when babies usually start crawling). For example, the babies born in January (on average) had their first crawl at age 29.84 weeks, and the average temperature 6 months after January (that’s July) was 66 degrees. We would record this data point as (66 degrees, 29.84 weeks). This was done for all 12 months, so there are 12 data points.
We want to investigate if the average age at which infants begin to crawl (y) can be predicted from the average outdoor temperature (x) six months after birth when they 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
y = mean of the values of y = 31.77
x s = standard deviation of the values of x = 15.85
y s = standard deviation of the values of y = 1.76
3. The slope of the least-squares regression line is
a. – 0.08. b. 0.49.
c. –1.58. d. 14.24.
4. The intercept of the least-squares regression line is
a. 0. b. 31.78.
c. – 31.78. d. None of the above.
5. Refer to the example data point (66 degrees, 29.84 weeks), referred to above. What is the residual
corresponding to this observation?
a. 29.84 weeks
b. 3.34 degrees
c. 26.5 weeks
d. 3.34 weeks