MATH 533 WEEK 7 COURSE PROJECT PART C,
REGRESSION AND CORRELATION
Project C
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.
It is evident that the slope for the ‘best fit’ line is positive, which indicates that sales
amount varies directly with calls. As calls 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 = 9.63795 + 0.201752 CALLS
, 3. Determine the coefficient of correlation. Interpret:
MINTAB Results:Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES and CALLS = 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.
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:
Since the significance level is α = 0.05 and we know that if the p-value is less than or equal
to the level of significance we reject the null hypothesis because the test statistic falls in the
rejection region. The p-value 0.000 is less than 0.05 so we will reject the null hypothesis
and accepting the alternative hypothesis and there is no significant correlation and in
conclusion the overall test of significance, the regression model is valid.
6. Based on your findings in 1-5, what is your opinion about using CALLS to predict
SALES? Explain.
After analyzing scatterplot for SALES vs. CALLS, calls is a great predictor of sales. As
calls increase the sales increases and they are correlated. Therefore, as the calls in the call
center increase, the company makes more money.
7. Compute the 95% confidence interval for beta-1 (the population slope).
REGRESSION AND CORRELATION
Project C
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.
It is evident that the slope for the ‘best fit’ line is positive, which indicates that sales
amount varies directly with calls. As calls 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 = 9.63795 + 0.201752 CALLS
, 3. Determine the coefficient of correlation. Interpret:
MINTAB Results:Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES and CALLS = 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.
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:
Since the significance level is α = 0.05 and we know that if the p-value is less than or equal
to the level of significance we reject the null hypothesis because the test statistic falls in the
rejection region. The p-value 0.000 is less than 0.05 so we will reject the null hypothesis
and accepting the alternative hypothesis and there is no significant correlation and in
conclusion the overall test of significance, the regression model is valid.
6. Based on your findings in 1-5, what is your opinion about using CALLS to predict
SALES? Explain.
After analyzing scatterplot for SALES vs. CALLS, calls is a great predictor of sales. As
calls increase the sales increases and they are correlated. Therefore, as the calls in the call
center increase, the company makes more money.
7. Compute the 95% confidence interval for beta-1 (the population slope).
