Correlation Coefficient: Regression Equation

        Correlation Coefficient Name Institution Date   Answer the following question: The following regression equation was computed from a sample of 20 observations: Y = 15 – 5X SSE was found to be 100 and SS total was 400. (a)   Determine the standard error of estimate;

• Standard Error is √ SSE/ (n-k)
• Where is the number of sample observations, which is 20
• K is the number of values in the sample, which is 2- as there is one dependent variable and  one independent variable
• SSE (error sum of squares) is the measure of unexplained variation or error variation and is represented as the residual in the ANOVA results and is 100

Standard Error=√100 (20-2) = √100/18=√5.5556= 2.3570 Explanation The standard error of estimate helps to determine how close the actual values are to the regression line. The standard error of estimate is most accurate when the data is normally distributed as outliers do not skew the data (Wright & Herrington, 2011).  The smaller the standard error of estimate the closer the variable of the regression line and as the error variation is small so is the standard error of estimate.  Similarly, when there is a larger sample size this reduces the standard errors of estimate as there are fewer unexplained variations.  The statistics further tells whether the sample represents the population and the dispersion or the variables in the regression.  If one was to fit the regression line, then the distance of the data points from the line would be 2.36% of the dependent variable. (b) Determine the coefficient of determination

• R square (R²⁾= SSR/ SST=SSR/ (SSR+SSE)
• The SSR is SST-SSE=400-100=300
• So R²=300/400=0.75

Explanation             In the calculation, the coefficient of determination is the ratio of the explained variation to the total variation. The measure determines the variability of a variable and how this explains the variation of one variable to the other.  The coefficient measures the variations of the dependent variable as explained by the variations in the predictors (Keller, 2016). For the sample, 75% of the variation in the outcome is explained by the regression model, and ...