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Linear Regression

Beginning with the Sum of Squared Error, which is defined as the inherent random variation or error. This is the region in which we can be wrong and we try to minimize. The numbers in this portion of our project are very large because we were dealing with 5 digit numbers to begin. The SSE=5,692,238,154. The next thing we look at is the Sum of Squared Regression, which can be defined as representing the difference between the predicted value of Y and the average value of Y. This value located under the SS column vertically and horizontally under the regression column = 2,473,481,862. The last of the three the Sum of Squared total variation is the measure of variation of the Yi values around their mean. This value is also found under the SS column and is horizontally located in the total column and it =8,165,720,016. These numbers are very important because they go along with the regression equation and represent the possible error.
             Two other important values that are found on the print out are the R-squared and R-value. The R-squared value is located under R-Sq on the print out and this equals 30.3%. This represents the measure of the proportion of variation in Y that is explained by the independent variable in the regression model. We can find this value using the equation R-squared=SSR/SST. In order to get R we then just have to take the Square root of .303 and we get .55. The r-value tells us the strength of the relationship between the two sets of variables. From looking at the number .55 we can tell that it is a positive relationship but it isn't extremely strong. It is about halfway in the positive relationship section so it is an average strength. .
             From using the numbers on the print out there are some tests that we can run to see if we have a linear relationship between the numbers and see a if correlation exists. The first of the three tests I ran is the t test for slope.


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