Regression Statistics. Accounting, Finance, SPSS Coursework (Coursework Sample)
The writer was required to complete a set of statistical questions pertaining to regression analysis. These include calculation of the coefficient of determination, adjusted sum of squares, and adjusted mean squares to complete the anova source table of a regression output.
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Homework 2: Regression Statistics
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Homework 2: Regression Statistics
Question 1
Part (a)
The slope or gradient of a straight-line relationship ranges between -1 and + 1. When the slope is negative, then an inverse relationship exists between X and Y. On the other hand, a positive slope means that X and Y variables have a direct relationship. However, when the estimated slope is equal to zero, it means there exists no inverse or direct relationship between X and Y. Hence, the trend line would traverse the graph horizontally as shown in the figure below.
Slope (β) = 0XYSlope (β) = 0XY
Part (B)
The slope of a linear relationship graph measures the rate of change in the outcome variable (y) when the input variable (X) changes. When the slope is a negative, it means that a change in X causes a corresponding decline on Y. On the other hand, a positive slope means that changes in X result in Y variable increasing. Therefore, it can be said that a linear relationship exists between X and Y variable as long as the slope is not equal to zero. In this case, linearity is a measure of the cause-effect relationship between the dependent and independent variable. Therefore, it the slope is equal to zero, as shown in the graph above, then a linear relationship does not exist at all.
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