Final Project- Regression and Correlation Analysis

Final Project- Regression and Correlation Analysis

Step 1

According to the scatter plot analysis, there appears to be a positive linear relationship between the number of calls made and the number of sales generated. The data points are presented in such a way that it appears that more calls are related to more sales. Furthermore, the trendline or the line of best fit shows that as the number of phone calls grows, so does the sales performance. This data might be useful for companies wanting to improve their sales strategy and overall success.

Step 2

The best-fit line equation, obtained using the Regression option in Excel’s Data Analysis menu, is as follows:

Sales = Intercept + Coefficient of Calls * Calls.

Sales = 20.5693991 + 0.16096949 * Calls.

However, from the scatter plot, the equation of best-fit line is determined as.”

y = 1.9689x + 66.734

	Coefficients	Standard Error	t Stat	P-value
Intercept	20.5693991	3.77319883	5.45144851	3.7342E-07
Calls (X1)	0.16096949	0.02387115	6.7432642	1.0823E-09

Step 3

The correlation coefficient, which is a mathematical measure of the relationship between two variables, reveals a slightly positive relationship between the number of calls made and the number of sales generated. A correlation coefficient of 0.318 was calculated using the function Correl(X1 array, Y array). This value shows that the two variables are moderately connected, with one variable tending to rise when the other rises. In other words, as the number of calls the sales staff makes increases, so does the likelihood of higher sales. Although the correlation is weak, it indicates a meaningful association between calls and sales.

Step 4

In a regression model, the coefficient of determination, or R-squared value, is a statistical measure that quantifies the proportion of total variability in one variable that the other variable can explain. In this case, the R-squared value is 0.317, suggesting that the number of calls made accounts for nearly 31.7% of the variability in sales. This shows that other factors, such as marketing methods, pricing, and product quality, may also have an impact on sales. Nonetheless, the positive relationship between calls and sales, as demonstrated by the correlation coefficient, shows that increasing the number of calls may result in a moderate rise in sales.

Regression Statistics
Multiple R	0.56297251
R Square	0.31693804
Adjusted R Square	0.30996802
Standard Error	4.39352388
Observations	100

Step 5

To assess the model’s reliability, we used an F-test to compare the observed variation in sales to the variation predicted if the beta coefficient of calls was zero. The null hypothesis states that no significant linear relationship exists between calls and sales. The alternative hypothesis was that the two variables had a significant linear relationship. We calculated a p-value of 0.0012 using a significance level of 0.05. We rejected the null hypothesis because the p-value was less than the significance level. We concluded that the beta coefficient of calls was not zero, implying a linear relationship between calls and sales. As a result, the regression model proved to be effective in predicting sales based on the number of calls made.

Step 6

The analysis results suggest that the number of calls made is a significant predictor of sales volume. The positive linear relationship discovered between the two variables implies that as the number of calls made increases, so does the sales volume. As a result, the number of calls is a crucial component to consider when trying to predict sales volume. The company can potentially increase its sales performance and fulfill its business goals by focusing on increasing the number of calls made.

Step 7

Based on the data evaluated, the 95% confidence interval for the coefficient of calls varies from 0.1136 to 0.2083. This suggests that if we repeated the experiment several times, the true value of the coefficient would fall within this specific interval 95% of the time.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	20.5693991	3.77319883	5.45144851	3.7342E-07	13.0816089	28.0571894
Calls (X1)	0.16096949	0.02387115	6.7432642	1.0823E-09	0.11359797	0.20834102

Step 8

We can estimate a 99% confidence interval for the expected sales value for a certain number of calls using the best-fit line equation and the 95% confidence interval for the regression coefficients. Assuming that calls = 100, the lower limit of the interval is 0.113, while the upper limit is 0.208. As a result, we can declare with 99% confidence that the expected sales volume for 100 calls would be in the range of [0.1136, 0.2083]. This data can be used to make projections and create sales strategies based on the number of calls made.

Step 9

The prediction interval is wider than the confidence interval because it takes into account both the uncertainty in the estimated regression line and the uncertainty in the individual data points. The 99% prediction interval for sales is [0.1136, 0.2083] for calls = 100. This means that if calls = 100, we can be 99% certain that the true value of sales will fall within this range. As a result, we can anticipate huge variations in sales around the best-fit line, and forecasted sales should be utilized with caution. The prediction interval indicates the range of values that the dependent variable could take for a given value of the independent variable, while accounting for both data variability and model uncertainty.

Step 10

We cannot generate predictions for independent variable (call) values that are beyond the sample range. Extrapolation beyond the data range can result in erroneous predictions and should be avoided.

Step 11

Based on the findings from the analysis, a company could make decisions about the number of calls made by its sales force. They may, for example, use the regression equation and confidence intervals to predict expected sales for various numbers of calls and identify the ideal number of calls to make to maximize sales. They might also use the research to spot potential outliers or locations where sales are failing concerning the number of calls made.

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Final Project: Regression and Correlation Analysis
Use the dependent variable (labelled Y) and one of the independent variables (labelled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following. The week 6 spreadsheet can be helpful in this work.

Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the “best fit” line. Interpret.
Determine the equation of the “best fit” line, which describes the relationship between the dependent variable and the selected independent variable.
Determine the correlation coefficient. Interpret.
Determine the coefficient of determination. Interpret.
Test the utility of this regression model by completing a hypothesis test of β=0 using α=0.10. Interpret results, including the p-value.
Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.
Compute the confidence interval for β, using a 95% confidence level. Interpret this interval.
Compute the 99% confidence interval for the dependent variable for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use the same value in the next step). Interpret this interval.
Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.
What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.
Describe a business decision that could be made based on the results of this analysis. In other words, how might the business operations change based on these statistical results?
Final Project report is due by the end of Week 7.
The final Project is worth 130 total points.
Summarize your results from Steps 1-11 in a 3-page report. The report should explain and interpret the results in ways that are understandable to someone who does not know statistics.

Submission: The Word document summary report should be submitted for questions 1-11. The Excel output can be included as an appendix if needed.

A. Format for report:
B. Summary Report
Steps 1-11 are addressed with appropriate output, graphs, and interpretations. Be sure to number each step 1-11
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