You must take the data from your problem and first decide the "best fit" for the data: linear, quadratic, or exponential and then proceed to graph the data, find a "regression" equation to fit the data, then answer questions predicting other values. The following table represents the median age at which men had their first marriage by years:
YEAR MALE (MEDIAN AGE)
1890 26.1
1900 25.9
1910 25.1
1920 24.6
1930 24.3
1940 24.3
1950 22.8
1960 22.8
1970 23.2
1980 24.7
1990 26.1
1995 26.9
1998 26.7
By inspection of the data in the above table, the median age is generally decreasing from 1890 and 1950, and then increasing from 1950 to 1998. This pattern is not consistent with either a linear or an exponential distribution, leaving only quadratic from the three given options.
A new table, which uses the years since 1890 as the independent variable is shown below:
Years Since 1890 MALE (MEDIAN AGE)
0 26.1
10 25.9
20 25.1
30 24.6
40 24.3
50 24.3
60 22.8
70 22.8
80 23.2
90 24.7
100 26.1
105 26.9
108 26.7
A scatter plot of the data is shown below:
(a) use your equation to predict the median age for the year 1946.
(b) use your equation to predict the year when the median age is 30