Part C: Regression and Correlation Analysis, statistics homework help

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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.

  1. Generate a scatterplot for the specified dependent variable (Y) and the X1 independent variable, including the graph of the "best fit" line. Interpret.
  2. Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.
  3. Determine the coefficient of correlation. Interpret.
  4. Determine the coefficient of determination. Interpret.
  5. Test the utility of this regression model. Interpret results, including the p-value.
  6. Based on the findings in Steps 1-5, analyze the ability of the independent variable to predict the designated dependent variable.
  7. Compute the confidence interval for β1 (the population slope) using a 95% confidence level. Interpret this interval.
  8. Using an interval, estimate the average for the dependent variable for a selected value of the independent variable. Interpret this interval.
  9. Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable. Interpret this interval.
  10. 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.

  1. Using Excel, run the multiple regression analysis using the designated dependent and three independent variables. State the equation for this multiple regression model.
  2. Perform the Global Test for Utility (F-Test). Explain the conclusion.
  3. 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.
  4. Is this multiple regression model better than the linear model generated in parts 1-10? Explain.
  5. NO plagiarism

Summarize your results from Steps 1–14 in a three-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 1–14 (Excel output and interpretations) as an appendix

Format for report:

  1. Summary Report
  2. Points 1–14 should be addressed with appropriate output, graphs, and interpretations. Be sure to number each point 1–14.

Unformatted Attachment Preview

Location Income ($1,000) Urban 27 Rural 25 Suburban 25 Suburban 26 Rural 30 Urban 29 Rural 33 Urban 30 Suburban 32 Urban 34 Urban 35 Urban 40 Rural 30 Rural 33 Urban 42 Suburban 32 Urban 43 Urban 43 Rural 33 Urban 47 Suburban 35 Urban 54 Suburban 42 Rural 36 Urban 57 Suburban 44 Rural 38 Urban 54 Urban 54 Suburban 46 Rural 40 Urban 60 Urban 58 Urban 61 Urban 61 Urban 62 Suburban 49 Urban 68 Suburban 57 Rural 45 Urban 71 Suburban 57 Suburban 64 Rural 45 Urban 74 Suburban 65 Rural 47 Rural 53 Suburban 66 Suburban 69 Size 1 4 1 1 5 1 6 1 2 1 1 1 6 6 2 2 2 2 7 2 3 2 3 7 3 3 7 3 3 4 7 4 4 5 5 6 5 6 6 8 7 7 8 8 7 8 8 8 8 8 Years 2 2 1 2 5 3 10 4 4 6 8 9 9 11 10 4 10 10 13 10 5 11 5 13 11 6 15 8 10 6 15 11 10 13 13 14 8 14 8 16 15 9 9 17 19 10 18 18 10 10 Credit Balance($) 2.631 2.047 3.155 3.913 2.660 3.531 2.766 3.769 4.082 3.806 4.049 4.073 2.697 2.914 4.073 4.310 4.199 4.253 3.104 4.293 4.456 4.340 4.925 3.178 4.391 4.947 3.203 4.354 4.366 5.003 3.250 4.402 4.397 4.595 4.786 4.888 5.148 5.011 5.220 3.257 5.528 5.283 5.332 3.304 5.553 5.484 3.342 3.788 5.756 5.861 Employee Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 SALES 46 34 44 45 42 47 33 44 42 37 46 40 43 52 41 42 32 42 38 49 39 43 50 37 39 43 44 45 40 43 42 48 44 51 37 37 46 44 41 42 40 37 47 39 40 37 35 44 CALLS 171 134 165 186 180 184 126 172 161 149 181 145 140 198 149 168 124 149 135 185 154 149 193 153 152 170 192 165 150 174 168 178 164 191 139 138 171 170 153 154 144 134 177 157 134 131 129 183 TIME 12.7 17.0 15.7 13.0 14.8 12.4 20.2 14.4 13.9 15.4 12.2 16.0 17.0 13.5 17.3 12.9 17.5 16.5 18.2 18.6 18.3 15.6 13.2 18.7 15.0 14.7 14.6 16.4 15.3 15.6 15.0 15.1 16.5 11.8 14.4 17.7 15.9 11.2 18.0 15.1 14.0 16.9 17.2 14.5 20.2 18.3 18.4 15.1 YEARS 5 4 3 3 2 2 3 3 1 3 4 0 2 2 0 3 2 1 1 2 1 1 1 0 3 4 1 3 3 2 0 3 3 2 0 1 5 0 3 2 3 2 0 4 3 1 4 4 TYPE ONLINE NONE ONLINE ONLINE ONLINE ONLINE NONE GROUP GROUP NONE ONLINE NONE GROUP ONLINE ONLINE ONLINE NONE GROUP GROUP ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE GROUP ONLINE NONE NONE ONLINE ONLINE GROUP GROUP NONE NONE ONLINE NONE GROUP GROUP NONE ONLINE 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 43 42 48 37 41 43 40 42 43 39 41 46 40 44 44 41 43 46 43 47 49 45 48 37 40 44 41 52 49 48 39 41 38 40 48 47 38 38 45 39 49 41 36 42 41 45 38 41 44 169 155 182 143 157 167 142 168 175 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 143 159 149 151 186 194 152 146 188 139 201 156 132 161 152 178 157 154 156 14.0 16.0 12.8 12.0 13.5 14.8 15.8 12.1 14.8 18.0 17.9 16.6 13.6 14.1 20.9 13.4 11.2 12.1 18.3 13.1 11.4 14.0 14.6 15.8 14.6 14.8 17.4 14.9 12.0 13.3 15.5 18.8 14.7 16.6 13.1 13.1 14.2 19.7 10.0 19.3 12.5 11.8 19.5 16.3 14.6 16.4 16.4 14.3 21.6 5 2 2 1 1 3 2 2 2 2 1 2 4 3 2 3 4 1 2 1 4 2 0 1 2 2 1 1 2 1 2 2 2 2 1 2 4 2 2 3 1 3 2 3 1 2 3 1 0 GROUP ONLINE ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE ONLINE ONLINE GROUP ONLINE ONLINE ONLINE ONLINE GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE NONE ONLINE NONE GROUP ONLINE ONLINE GROUP NONE ONLINE GROUP ONLINE GROUP NONE ONLINE ONLINE ONLINE GROUP GROUP ONLINE 98 99 100 44 44 37 170 170 146 12.5 15.8 17.7 1 0 3 ONLINE ONLINE NONE Legend: Employee Number is just as it sounds. SALES represents the number sales made this week. CALLS represents the number of sales calls made this week. TIME represents the average time per call this week. YEARS represents years of experience in the call center. TYPE represents the type of training the employee received. Employee Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 SALES 46 34 44 45 42 47 33 44 42 37 46 40 43 52 41 42 32 42 38 49 39 43 50 37 39 43 44 45 40 43 42 48 44 51 37 37 46 44 41 42 40 37 47 39 40 37 35 44 CALLS 171 134 165 186 180 184 126 172 161 149 181 145 140 198 149 168 124 149 135 185 154 149 193 153 152 170 192 165 150 174 168 178 164 191 139 138 171 170 153 154 144 134 177 157 134 131 129 183 TIME 12,7 17,0 15,7 13,0 14,8 12,4 20,2 14,4 13,9 15,4 12,2 16,0 17,0 13,5 17,3 12,9 17,5 16,5 18,2 18,6 18,3 15,6 13,2 18,7 15,0 14,7 14,6 16,4 15,3 15,6 15,0 15,1 16,5 11,8 14,4 17,7 15,9 11,2 18,0 15,1 14,0 16,9 17,2 14,5 20,2 18,3 18,4 15,1 YEARS 5 4 3 3 2 2 3 3 1 3 4 0 2 2 0 3 2 1 1 2 1 1 1 0 3 4 1 3 3 2 0 3 3 2 0 1 5 0 3 2 3 2 0 4 3 1 4 4 TYPE ONLINE NONE ONLINE ONLINE ONLINE ONLINE NONE GROUP GROUP NONE ONLINE NONE GROUP ONLINE ONLINE ONLINE NONE GROUP GROUP ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE GROUP ONLINE NONE NONE ONLINE ONLINE GROUP GROUP NONE NONE ONLINE NONE GROUP GROUP NONE ONLINE 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 43 42 48 37 41 43 40 42 43 39 41 46 40 44 44 41 43 46 43 47 49 45 48 37 40 44 41 52 49 48 39 41 38 40 48 47 38 38 45 39 49 41 36 42 41 45 38 41 44 169 155 182 143 157 167 142 168 175 150 155 163 162 189 153 158 160 173 178 189 184 174 188 149 159 160 166 178 178 176 143 159 149 151 186 194 152 146 188 139 201 156 132 161 152 178 157 154 156 14,0 16,0 12,8 12,0 13,5 14,8 15,8 12,1 14,8 18,0 17,9 16,6 13,6 14,1 20,9 13,4 11,2 12,1 18,3 13,1 11,4 14,0 14,6 15,8 14,6 14,8 17,4 14,9 12,0 13,3 15,5 18,8 14,7 16,6 13,1 13,1 14,2 19,7 10,0 19,3 12,5 11,8 19,5 16,3 14,6 16,4 16,4 14,3 21,6 5 2 2 1 1 3 2 2 2 2 1 2 4 3 2 3 4 1 2 1 4 2 0 1 2 2 1 1 2 1 2 2 2 2 1 2 4 2 2 3 1 3 2 3 1 2 3 1 0 GROUP ONLINE ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE ONLINE ONLINE GROUP ONLINE ONLINE ONLINE ONLINE GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE NONE ONLINE NONE GROUP ONLINE ONLINE GROUP NONE ONLINE GROUP ONLINE GROUP NONE ONLINE ONLINE ONLINE GROUP GROUP ONLINE 98 99 100 44 44 37 170 170 146 12,5 15,8 17,7 1 0 3 ONLINE ONLINE NONE Legend: Employee Number is just as it sounds. SALES represents the number sales made this week. CALLS represents the number of sales calls made this week. TIME represents the average time per call this week. YEARS represents years of experience in the call center. TYPE represents the type of training the employee received. SALES 46 34 44 45 42 47 33 44 42 37 46 40 43 52 41 42 32 42 38 49 39 43 50 37 39 43 44 45 40 43 42 48 44 51 37 37 46 44 41 42 40 37 47 39 40 37 35 44 43 42 48 Ho Ha mu=41.5 mu>41.5 alpha 0,05 xbar 42,34 sd 4,1711 n 100 std.error 0,417 t-value 2,014 Rejection region Reject Ho,if t> p-value 95% Confidence Interval Lower Limit Upper Limit 0,0234 41,51 43,17 1,6604 37 41 43 40 42 43 39 41 46 40 44 44 41 43 46 43 47 49 45 48 37 40 44 41 52 49 48 39 41 38 40 48 47 38 38 45 39 49 41 36 42 41 45 38 41 44 44 44 37 Mean sales per week exceeds 41.5 per salesperson b. SALES Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level(95.0%) 42,34 0,4171137 42 44 4,1711 17,3984 -0,2171 0,0726 20 32 52 4234 100 0,8276 5 per salesperson TYPE ONLINE NONE ONLINE ONLINE ONLINE ONLINE NONE GROUP GROUP NONE ONLINE NONE GROUP ONLINE ONLINE ONLINE NONE GROUP GROUP ONLINE NONE ONLINE ONLINE NONE GROUP GROUP GROUP ONLINE GROUP ONLINE ONLINE ONLINE GROUP ONLINE NONE NONE ONLINE ONLINE GROUP GROUP NONE NONE ONLINE NONE GROUP GROUP NONE ONLINE GROUP ONLINE ONLINE Proportion receiving online training is l n online phat std.error Reject Ho if z
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Explanation & Answer

Hi,I showed my work both on excel and appendix.Let me know if you have any doubt.Thankyou.

CALLS(X1) SALES(Y)
171
46
134
34
165
44
186
45
180
42
184
47
126
33
172
44
161
42
149
37
181
46
145
40
140
43
198
52
149
41
168
42
124
32
149
42
135
38
185
49
154
39
149
43
193
50
153
37
152
39
170
43
192
44
165
45
150
40
174
43
168
42
178
48
164
44
191
51
139
37
138
37
171
46
170
44
153
41
154
42
144
40
134
37
177
47
157
39
134
40
131
37
129
35
183
44
169
43
155
42
182
48

143
157
167
142
168
175
150
155
163
162
189
153
158
160
173
178
189
184
174
188
149
159
160
166
178
178
176
143
159
149
151
186
194
152
146
188
139
201
156
132
161
152
178
157
154
156
170
170
146

37
41
43
40
42
43
39
41
46
40
44
44
41
43
46
43
47
49
45
48
37
40
44
41
52
49
48
39
41
38
40
48
47
38
38
45
39
49
41
36
42
41
45
38
41
44
44
44
37

Simple Linear Regression Analysis
Regression Statistics
Multiple R
0,8713
R Square
0,7592
Adjusted R Square 0,7568
Standard Error
2,0571
Observations
100

Calculations
b1, b0 Coefficients
b1, b0 Standard Error
R Square, Standard Error
F , Residual df
Regression SS , Residual SS
Confidence level
t Critical Value
Half Width b0
Half Width b1

0,2018
0,0115
0,7592
309,0460
1307,7471
95%
1,9845
3,7140
0,0228

9,6380
1,8716
2,0571
98,0000
414,6929

Employee Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48

SALES(Y)
46
34
44
45
42
47
33
44
42
37
46
40
43
52
41
42
32
42
38
49
39
43
50
37
39
43
44
45
40
43
42
48
44
51
37
37
46
44
41
42
40
37
47
39
40
37
35
44

CALLS(X1)
171
134
165
186
180
184
126
172
161
149
181
145
140
198
149
168
124
149
135
185
154
149
193
153
152
170
192
165
150
174
168
178
164
191
139
138
171
170
153
154
144
134
177
157
134
131
129
183

TIME(X2)
12,7
17,0
15,7
13,0
14,8
12,4
20,2
14,4
13,9
15,4
12,2
16,0
17,0
13,5
17,3
12,9
17,5
16,5
18,2
18,6
18,3
15,...


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I was having a hard time with this subject, and this was a great help.

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