Answer
The equation for the regression line is $\left( 1.04027 \right)M=x+35.089$ for males and $\left( 1.12696 \right)F=x+24.0775$ for females.
Work Step by Step
The objective is to fit a regression line for the provided data.
First, use the percentage of males that are never married.
To fit a regression line for the given data, use a Ti-83 calculator and follow the steps given below:
Step1: Press “2nd” and “0” key; catalog window will open; move the cursor to “Diagnostic On;” press “Enter;” again press “Enter.”
Step2: Press “Stat” key, scroll to “1:Edit” and press “Enter.” Enter the values of the independent variables x in the list ${{L}_{1}}$ and the corresponding values of the dependent variable y in the list ${{L}_{2}}$.
$\begin{align}
& {{L}_{1}}=31.1,45.2,51.7,62.6 \\
& {{L}_{2}}=0,10,20,30 \\
\end{align}$
Step3: Press “Stat key” and then the right arrow key and move to “CALC.” Scroll to “4:LinReg” and press “Enter” and again press “Enter.”
$\begin{align}
& x=a+bM \\
& a=-35.089244 \\
& b=1.040275 \\
\end{align}$
This shows that the equation for the regression line is:
$\begin{align}
& x=\left( -35.089 \right)+\left( 1.04027 \right)M \\
& \left( 1.04027 \right)M=x+35.089
\end{align}$
Here, $x$ represents the number of years after 1980 and $M$ represents the percentage of males that are never married.
Now, follow the same procedure for females.
The objective is to fit a regression line for the data.
At first, use the percentage of females that are never married by the steps given below:
Step1: Press “2nd” and “0” key; catalog window will open; move the cursor to “Diagnostic On;” press “Enter;” again press “Enter.”
Step2: Press “Stat” key, scroll to “1: Edit” and press “Enter.” Enter the values of the independent variables x in list ${{L}_{1}}$ and the corresponding values of the dependent variable y in list ${{L}_{2}}$.
$\begin{align}
& {{L}_{1}}=20.9,31.1,38.9,47.8 \\
& {{L}_{2}}=0,10,20,30 \\
\end{align}$
Step3: Press “Stat key” and then the right arrow key and move to “CALC.” Scroll to
“4: LinReg” and press “Enter” and again press “Enter.”
$\begin{align}
& x=a+bF \\
& a=-24.0775 \\
& b=1.12696 \\
\end{align}$
This shows that the equation for the regression line is:
$\begin{align}
& x=\left( -24.0775 \right)+\left( 1.12696 \right)F \\
& \left( 1.12696 \right)F=x+24.0775
\end{align}$
Here, $x$ represents the number of years after 1980 and $F$ represents the percentage of females that are never married.
It can be predicted from the above results that the percentage of males and females that are never married increases linearly with the year.
Circumstances in which the prediction may vary:
a. The data will saturate and will not follow a linear equation because the population of the state will come to a standstill if the percentage of both the unmarried males and females goes on increasing.
b. The percentage may go down once the males and females attain their suitable age for marriage.
