Question

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 data below, thank you for helping me with this in advance, I really appreciate it.

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 |

Answer #1

Data

Type is made cateogrical

1 for online, 2 for group , 0 for none

result for multiple regression

SUMMARY OUTPUT | |||||||

Regression Statistics | |||||||

Multiple R | 0.693545406 | ||||||

R Square | 0.48100523 | ||||||

Adjusted R Square | 0.459152819 | ||||||

Standard Error | 3.480531964 | ||||||

Observations | 100 | ||||||

ANOVA | |||||||

df | SS | MS | F | Significance F | |||

Regression | 4 | 1066.600238 | 266.6500595 | 22.01154018 | 7.04189E-13 |
||

Residual | 95 | 1150.839762 | 12.11410276 | ||||

Total | 99 | 2217.44 | |||||

Coefficients | Standard Error | t Stat | P-value |
Lower 95% | Upper 95% | Lower 95.0% | |

Intercept | 20.07981678 | 4.515261657 | 4.447099261 | 2.36175E-05 |
11.11588904 | 29.04374451 | 11.11588904 |

TYPE | -0.085965801 | 0.463839992 | -0.185335036 | 0.853361379 |
-1.006804611 | 0.834873008 | -1.006804611 |

Calls (X1) | 0.171766931 | 0.020281269 | 8.469239868 | 3.06065E-13 |
0.131503522 | 0.21203034 | 0.131503522 |

Time (X2) | -0.133904863 | 0.131953162 | -1.014790864 | 0.312783101 |
-0.395865011 | 0.128055284 | -0.395865011 |

Years (X3) | -0.257125411 | 0.294252939 | -0.873824446 | 0.384417446 |
-0.841291353 | 0.327040531 | -0.841291353 |

significance F = **7.04189E-13 << 0.05**

hence this model is significance

if p-value < 0.05 , that variable is significant

here only X1 has p-value (**3.06065E-13)** <
0.05

we can keep X1 and remove X2,x3 and type

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...

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Sample #
Observations
Defects
1
44
49
44
44
40
0
2
42
46
51
51
42
2
3
45
45
49
49
46
2
4
40
39
42
42
47
7
5
44
51
53
53
44
2
6
41
44
43
43
46
8
7
40
44
46
46
48
3
8
54
49
48
48...

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y
x1
x2
x3
x4
x5
96
8
60
2.4
48
51
73
6
64
2.1
42
43
108
2
76
1.8
34
20
124
5
74
2.2
11
14
82
6
50
1.5
61
29
89
9
57
1.6
53
22
76
1
72
2
72
38
109
3
74
2.8
36
40
123
2
99
2.6
17
50
125
6
81
2.5
48
55
101
2...

y x1 x2 x3
x4
64 74 22 24
17
43 63 29 15
30
51 78 20 9 25
49 52 17 38
29
39 45 12 19 37
Consider the set of dependent and independent variables given
below. Perform a best subsets regression and choose the most
appropriate model for these data.
Find the most appropriate model for the data. Note that the
coefficient is 0 for any variable that is not included in the
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y= _____+...

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17 212 Round your all answers to two decimal places. Enter negative
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Consider the following data for a dependent variable y and two
independent variables, x1 and x2.
x1
x2
y
29
12
95
46
10
109
24
17
113
50
17
178
40
5
94
52
19
176
74
7
170
36
13
118
59
13
143
76
16
212
Round your all answers to two decimal places. Enter negative
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a. Develop an estimated regression equation
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Actual Y
X1
X2
Predicted Y
Prediction Error
6
6.8
4.7
3.1
5.3
5.5
5.8
4.5
6.2
4.5
8.8
7
4.5
6.8
6.1
3.7
8.5
5.1
5.4
8.9
4.8
5.1
6.9
5.4
5.8
9.3
5.9
5.7
8.4
5.4

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44
47
31
45
48
32
50
43...

Consider the following data for a dependent variable y
and two independent
variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for these data isŷ =
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4.74x2.
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