PROJECT PART C: Regression and Correlation Analysis
MATH533: Applied Managerial Statistics
PROJECT PART C: Regression and Correlation Analysis
Using MINITAB perform the regression and correlation analysis for the data on SALES (Y) and CALLS (X), by answering the following questions:
1. Generate a scatterplot for SALES vs. CALLS, including the graph of the "best fit" line. Interpret.
After interpreting the scatter plot, it is evident that the slope of the ‘best fit’ line is positive, which indicates that sales amount varies directly with calls. As call increases, the sales amount increases as well.
2. Determine the equation of the "best fit" line, which describes the relationship between SALES and CALLS.
The equation of the ‘best fit’ line or the regression equation is SALES(Y) = 9.638 + 0.2018 CALLS(X1)
3. Determine the coefficient of correlation. Interpret:
MINTAB Results:
Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES(Y) and CALLS(X1) = 0.871
P-Value = 0.000
The coefficient of correlation is 0.871. The correlation coefficient is positive so this indicates a positive or direct relationship between the variables. The correlation coefficient is far from the P-Value of 0.000. This means that there is an extremely low chance that Sales and Calls results are wrong and we can be confident in interpretation.
4. Determine the coefficient of determination. Interpret.
MINTAB Results: S = 2.05708 R-Sq = 75.9% R-Sq(adj) = 75.7%
The index of determination is the r-square = 0.759. The coefficient of determination is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable, which for this regression model is 75.9%.
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.
MINTAB Results:
Coefficients:
Term Coef SE Coef T P 95% CI
Constant
PROJECT PART C: Regression and Correlation Analysis
Using MINITAB perform the regression and correlation analysis for the data on SALES (Y) and CALLS (X), by answering the following questions:
1. Generate a scatterplot for SALES vs. CALLS, including the graph of the "best fit" line. Interpret.
After interpreting the scatter plot, it is evident that the slope of the ‘best fit’ line is positive, which indicates that sales amount varies directly with calls. As call increases, the sales amount increases as well.
2. Determine the equation of the "best fit" line, which describes the relationship between SALES and CALLS.
The equation of the ‘best fit’ line or the regression equation is SALES(Y) = 9.638 + 0.2018 CALLS(X1)
3. Determine the coefficient of correlation. Interpret:
MINTAB Results:
Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES(Y) and CALLS(X1) = 0.871
P-Value = 0.000
The coefficient of correlation is 0.871. The correlation coefficient is positive so this indicates a positive or direct relationship between the variables. The correlation coefficient is far from the P-Value of 0.000. This means that there is an extremely low chance that Sales and Calls results are wrong and we can be confident in interpretation.
4. Determine the coefficient of determination. Interpret.
MINTAB Results: S = 2.05708 R-Sq = 75.9% R-Sq(adj) = 75.7%
The index of determination is the r-square = 0.759. The coefficient of determination is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable, which for this regression model is 75.9%.
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.
MINTAB Results:
Coefficients:
Term Coef SE Coef T P 95% CI
Constant