a. The linear model fits the data moderately well due to the high correlation coefficients and positive scatterplots. b. The slopes for the functions M and F are 20.233 and 28.687, respectively. c. The slope of 28.687 indicates a sharper increase in females earning bachelor's degrees.
a. The linear model fits the data moderately well because the correlation coefficients for men and women are both extremely close to 1.
This indicates a strong positive correlation between time and degrees earned for both genders.
Additionally, the scatterplots show a positive correlation, further supporting the fit of the linear model.
b. The slope for the function M is 20.233, and the slope for the function F is 28.687.
These slopes represent the annual increase in degrees earned for men and women, respectively.
c. The slope of 28.687 for females indicates that for every year, there is a sharper increase in the number of females earning bachelor's degrees compared to males.
The probable question may be:
Interpreting the regression equations for the relationship between time and degrees earned. a. Often, social changes, such as education trends, show linear relationships. How well does a linear model fit the data in this problem? Justify your answer in terms of the scatterplots and in terms of the data that the regression calculator gives. Both scatterplots show a positive correlation. For men, and, for women, . The linear model fits the data moderately well, because .991 and .983 are extremely near to 1.
b. Using proper units, state the slopes for the functions M and F .
Slope of M: 20.233
Slope of F: 28.687
c. Explain what these slopes represent in terms of Americans earning bachelor degrees. Every year, there is a sharper increase of females earning bachelor degrees than males