Answer:
The graph is below.
Step-by-step explanation:
Linear regression is a linear approach to modelling the relationship between a dependent variable and one or more independent variables.
Let X be the independent variable and Y be the dependent variable. We will define a linear relationship between these two variables as follows:
[tex]Y=bX+a[/tex]
We have the following data:
[tex]\left\begin{array}{cc}\mathrm{SAT \:Score}&\mathrm{College GPA}\\650&2.43\\986&3.0\\860&2.87\\1250&3.8\\1400&3.74\\1440&3.62\\622&2.3\\1050&3.18\\1170&3.3\\1560&3.92\end{array}\right \\[/tex]
To find the line of best fit for the points, follow these steps:
Step 1: Find [tex]X\cdot Y[/tex] and [tex]X\cdot X[/tex] as it was done in the table.
Step 2: Find the sum of every column:
[tex]\sum{X} = 10988 ~,~ \sum{Y} = 32.16 ~,~ \sum{X \cdot Y} = 36950.3 ~,~ \sum{X^2} = 13022280[/tex]
Step 3: Use the following equations to find intercept a and slope b:
[tex]\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 32.16 \cdot 13022280 - 10988 \cdot 36950.3}{ 10 \cdot 13022280 - 10988^2} \approx 1.348 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 10 \cdot 36950.3 - 10988 \cdot 32.16 }{ 10 \cdot 13022280 - \left( 10988 \right)^2} \approx 0.002\end{aligned}[/tex]
Step 4: Assemble the equation of a line
[tex]\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~1.348 ~+~ 0.002 \cdot x\end{aligned}[/tex]
The graph of the regression line is:
