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Mathematics & Economics
Math Problem
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Model Simple Linear Regression (Math Problem Sample)


This week’s assignment requires that you demonstrate the relationship between two variables.  You will be required to use the least squares approach as well as use software (SPSS preferred) to perform analyses that will yield the coefficient of correlation, the coefficient of determination, and a simple linear regression analysis.

Your submission should demonstrate thoughtful consideration of the ideas and concepts presented in the course.


Linear Regression
Author Name
Institution Affiliation
If I am to model the relationship between the mean or expected number of games won by a major-league team and the team’s batting average is x, then a straight line would be used and the slope of a line would be negative. This is because a negative slope line implies that y will decrease when x increases and vice versa. An example of a graph with negative slope is as follows:
Negative Slope
m =  =  = -  This indicates that when x increases by 3, then y decreases instantly by 4, and when x decreases by 3, then y increases automatically by 4.
The pattern revealed by the scattergram agrees with my answer to part a.
In order to construct a simple linear regression of the data, a linear relationship between the two variables should exist. Whilst there are a couple of ways to determine whether the linear relationship is present between the two variables or not, the best way is to create a scatterplot using SPSS in which the dependent variable can be plotted against the independent variable.
The eqaution of least squares line is ŷ= a + b x.
This graph reveals that the least squares line fits the point on my scattergram.
After looking at the data, I have found that the mean or expected number of games won is strongly related to a team’s batting average, as the two variables are positively related to one another and their highest values are also interlinked.
From the regression equation, I have seen that the straight line expression is 119.86 +0.346x. It is a reliable equation as the regression F value is <0.05. In the meantime, the value of  and  are 119.86 and 0.346 respectively. These values have been obtained from the regression table.
The equation of the least squares line for Brand A and Brand B is as follows:
y = mx + b
y = how far up
m = gradient or slope (how steep the line is)
x = how far long
b = the Y intercept (the line that crosses the Y axis)
For the first brand:
For the second brand:
I would like to use the least squares line to predict useful life for a given cutting speed for the second brand, as its value of y is better than the first brand’s value of y.
The equation of the least squares line is as follows:

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