Question

In: Statistics and Probability

Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the independent variables...

Regression and Correlation Analysis

Use the dependent variable (labeled Y) and one of the independent variables (labeled 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.

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 coefficient of correlation. Interpret.

Determine the coefficient of determination. Interpret.

Test the utility of this regression model, represented by a hypothesis test of b=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 b, 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 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.

Summarize your results from Steps 1–10 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 summary report and all of the work done in 1–10 (Excel output and interpretations) as an appendix

Format for report:

Summary Report

Steps 1-10 addressed with appropriate output, graphs and interpretations. Be sure to number each step 1-10.

Sales (Y) Calls (X1) Time (X2) Years (X3) Type
46 172 14.7 3 GROUP
42 161 13.2 1 GROUP
42 140 17.5 2 GROUP
38 135 18.5 1 GROUP
33 152 15.0 3 GROUP
31 170 14.3 4 GROUP
44 192 16.7 1 GROUP
39 150 15.3 3 GROUP
41 164 17.8 3 GROUP
49 153 19.0 3 GROUP
42 154 14.3 2 GROUP
44 134 19.4 5 GROUP
49 131 14.6 1 GROUP
43 169 14.0 5 GROUP
44 168 12.4 2 GROUP
43 175 13.6 5 GROUP
33 150 14.9 2 GROUP
32 155 17.9 1 GROUP
48 162 14.5 4 GROUP
49 178 18.3 2 GROUP
35 149 15.6 1 GROUP
44 159 14.6 2 GROUP
67 166 18.9 1 GROUP
47 151 16.6 2 GROUP
41 152 14.5 4 GROUP
33 139 19.3 3 GROUP
45 156 13.2 3 GROUP
50 157 15.9 3 GROUP
42 154 15.3 1 GROUP
20 210 8.0 1 NONE
32 139 16.9 4 NONE
32 120 19.9 3 NONE
33 143 15.4 3 NONE
55 160 17.0 3 NONE
36 121 18.0 2 NONE
67 155 17.9 1 NONE
37 159 18.1 0 NONE
37 132 10.0 0 NONE
36 140 15.7 1 NONE
37 142 13.9 3 NONE
37 130 16.9 2 NONE
39 160 14.3 4 NONE
35 130 19.4 4 NONE
39 140 12.4 1 NONE
50 144 15.8 2 NONE
45 138 15.3 2 NONE
40 145 14.7 2 NONE
29 145 19.0 2 NONE
36 131 18.5 2 NONE
39 144 17.7 3 NONE
44 165 15.7 3 ONLINE
47 186 13.5 3 ONLINE
41 180 14.0 2 ONLINE
35 150 13.0 4 ONLINE
42 181 11.5 4 ONLINE
41 198 13.2 2 ONLINE
41 149 17.3 0 ONLINE
44 168 11.0 5 ONLINE
30 125 11.0 5 ONLINE
21 185 18.9 2 ONLINE
45 149 13.5 1 ONLINE
52 193 13.7 5 ONLINE
44 165 12.4 3 ONLINE
43 174 12.7 2 ONLINE
42 168 16.4 0 ONLINE
49 178 15.1 3 ONLINE
40 191 19.0 5 ONLINE
46 171 14.9 5 ONLINE
41 170 12.3 0 ONLINE
21 177 17.0 0 ONLINE
46 183 15.4 4 ONLINE
41 155 16.0 2 ONLINE
48 182 13.0 2 ONLINE
40 157 15.4 1 ONLINE
48 167 14.8 3 ONLINE
46 163 16.6 2 ONLINE
56 189 15.0 3 ONLINE
44 153 15.3 2 ONLINE
34 158 14.2 3 ONLINE
43 160 10.9 4 ONLINE
33 173 17.5 1 ONLINE
50 189 14.3 1 ONLINE
52 184 11.4 4 ONLINE
45 174 13.6 2 ONLINE
48 188 13.6 0 ONLINE
44 160 14.8 2 ONLINE
51 178 16.5 1 ONLINE
41 178 13.4 2 ONLINE
40 176 12.6 1 ONLINE
41 159 18.8 2 ONLINE
48 186 14.2 1 ONLINE
42 194 13.6 2 ONLINE
48 188 11.3 2 ONLINE
48 201 12.5 1 ONLINE
43 161 17.3 3 ONLINE
42 152 14.6 1 ONLINE
49 178 16.4 2 ONLINE
44 156 20.0 0 ONLINE
45 170 14.2 1 ONLINE
48 170 17.4 5 ONLINE

Solutions

Expert Solution

Lets perform the analysis by going to data > data analysis tab and then selecting regression . Please see the below screenshots of the setup in excel along with the scatterplot

The regression line is formed using the regression coefficients as

Y = 19.26 +0.1121*X1 + 0.2673*X2 + 0.2387*X3

the coefficient of determination is

R Square 0.069835154

this means that the model is able to explain oonly 6% variation in Y due to variation in independent variables x1 , x2 and x3

The coefficient of correlation is

0.2642

P-value
Intercept 0.058399
Calls (X1) 0.009202
Time (X2) 0.42301
Years (X3) 0.663431

all the independnet variables whose p value is less than 0.1 are considered signficant for the model

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

orchestra answered 1 year ago
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