PROJECT PART C: Regression and Correlation Analysis Essay

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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
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Explain your answer.
MINTAB Results:
Descriptive Statistics: SALES(Y), CALLS(X1)

Variable N Mean SE Mean StDev Minimum Median Maximum
SALES(Y) 100 42.340 0.417 4.171 32.000 42.000 52.000
CALLS(X1) 100 162.09 1.80 18.01 124.00 160.50 201.00

Since the maximum value of the predictor variable (calls) is used to formulate the given regression model is 201.00, which is less than 300, we cannot use the given regression model to accurately estimate the weekly sales for weekly call of 300. So we can’t say anything about the weekly sales when weekly calls are 300.
In an attempt to improve this model, we attempt to do a multiple regression model predicting SALES based on CALLS, TIME, and YEARS.

11. Using MINITAB run the multiple regression analysis using the variables CALLS, TIME, and YEARS to predict SALES. State the equation for this multiple regression model.
MINTAB Results:
General Regression Analysis: SALES(Y) versus CALLS(X1), TIME(X2), YEARS(X3):
Regression Equation
SALES(Y) = 8.60864 + 0.20551 CALLS(X1) + 0.0520391 TIME(X2) - 0.181791 YEARS(X3)

Term Coef SE Coef T P 95% CI
Constant 8.60864 3.55193 2.4236 0.017 ( 1.55811, 15.6592)
CALLS(X1) 0.20551 0.01409 14.5811 0.000 ( 0.17753, 0.2335)
TIME(X2) 0.05204 0.10570 0.4923 0.624 (-0.15778, 0.2619)
YEARS(X3) -0.18179
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