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Part C: Regression and Correlation Analysis Use the dependent variable (labeled Y) and the independent variables...

Part C: Regression and Correlation Analysis

Use the dependent variable (labeled Y) and the independent variables (labeled X1, X2, and X3) in the data file. Use Excel to perform the regression and correlation analysis to answer the following.

Generate a scatterplot for the specified dependent variable (Y) and the X1 independent variable, 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 coefficient of correlation. Interpret.

Determine the coefficient of determination. Interpret.

Test the utility of this regression model. Interpret results, including the p-value.

Based on the findings in Steps 1-5, analyze the ability of the independent variable to predict the designated dependent variable.

Compute the confidence interval for β1 (the population slope) using a 95% confidence level. Interpret this interval.

Using an interval, estimate the average for the dependent variable for a selected value of the independent variable. Interpret this interval.

Using an interval, predict the particular value of the dependent variable for a selected value of the independent 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.

In an attempt to improve the model, use a multiple regression model to predict the dependent variable .Y, based on all of the independent variables. X1, X2, and X3.

Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.

Perform the Global Test for Utility (F-Test). Explain the conclusion.

Perform the t-test on each independent variable. Explain the conclusions and clearly state how the analysis should proceed. In particular, which independent variables should be kept and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and summarize results with discussion of analysis.

Is this multiple regression model better than the linear model generated in parts 1-10? Explain. Please use the actual data from below in the analysis.

Sales (Y) Calls (X1) Time (X2) Years (X3) Type
51 167 12.6 5 ONLINE
34 133 15.2 4 GROUP
49 161 16.1 3 NONE
45 185 13.3 1 ONLINE
47 176 14.1 2 ONLINE
47 183 12.8 2 ONLINE
38 122 19.3 3 GROUP
44 171 13.6 3 GROUP
47 157 14.3 1 GROUP
37 148 15.7 3 GROUP
51 177 11.4 4 NONE
40 144 17.4 0 NONE
48 136 13.3 2 ONLINE
52 197 14 2 ONLINE
46 145 16.8 0 ONLINE
42 167 17.7 3 ONLINE
37 120 12 2 NONE
42 148 16.9 1 NONE
43 131 18.5 1 NONE
49 184 16.7 2 ONLINE
44 150 18.4 1 NONE
43 148 15.9 1 ONLINE
55 189 12 1 ONLINE
37 152 19.8 0 GROUP
44 148 13.5 3 GROUP
43 169 13.3 4 NONE
49 188 20.4 1 NONE
45 164 16.7 3 NONE
45 146 12 3 GROUP
43 173 19.8 2 ONLINE
47 164 15.3 0 ONLINE
48 177 13.9 3 ONLINE
49 160 13.6 3 GROUP
51 190 11.3 1 ONLINE
42 135 16.1 0 NONE
37 137 18.1 1 ONLINE
51 167 16.2 1 ONLINE
44 169 8.9 0 ONLINE
46 149 17.8 3 NONE
42 153 15.5 2 GROUP
45 140 11 3 GROUP
37 133 19.8 2 NONE
52 173 18.6 0 ONLINE
39 156 13.3 4 NONE
45 130 20.6 3 GROUP
37 130 15.6 1 GROUP
40 125 12.2 4 NONE
44 182 15.5 4 NONE
48 165 19.8 5 ONLINE
42 154 14.8 2 ONLINE
53 178 13.2 2 ONLINE
37 142 18.5 1 NONE
46 153 14.1 1 ONLINE
43 166 17.6 3 ONLINE
45 138 18.9 2 NONE
42 167 18 2 NONE
48 171 13 2 GROUP
39 149 18.8 1 GROUP
46 151 16 1 GROUP
46 162 16.2 2 ONLINE
45 158 13.9 1 ONLINE
44 188 12.9 3 GROUP
49 149 21.1 2 GROUP
41 157 11.5 3 ONLINE
48 156 15.1 4 ONLINE
46 172 12.5 1 ONLINE
48 174 18.6 2 GROUP
47 188 16.3 1 NONE
54 180 11.8 4 GROUP
45 173 17.6 2 ONLINE
53 184 15.2 0 ONLINE
37 148 16.2 1 GROUP
45 155 18.9 2 GROUP
44 159 18.1 2 ONLINE
46 162 12.1 1 GROUP
52 177 14.5 1 ONLINE
54 174 10.8 2 NONE
48 175 13.7 1 ONLINE
44 139 15.2 2 NONE
41 158 19.3 2 ONLINE
43 145 18.6 2 NONE
40 150 10.8 1 GROUP
53 182 10.5 1 ONLINE
47 193 13.5 2 ONLINE
43 148 14.5 4 ONLINE
38 145 17.1 2 NONE
50 184 15.6 2 ONLINE
39 138 17.7 3 GROUP
54 197 11.8 1 ONLINE
41 155 13.6 3 GROUP
41 128 15.5 2 NONE
42 160 10.6 3 NONE
46 148 13.1 1 GROUP
45 177 14.2 2 GROUP
43 153 15.2 3 GROUP
41 153 14.7 1 GROUP
49 152 22.3 0 ONLINE
44 169 13.6 1 ONLINE
49 166 16.2 0 ONLINE
37 145 18 3 NONE
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

From above ANOVA table it is clear that overall regression is significant. Also it is seen that only Calls(X1) affects on the sales(Y1)

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