Question

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 |

Answer #1

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...

Please compute the value, upper control limit, and lower
control limit for the x-bar chart, r-bar chart, p
chart, and np chart.
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...

A sample of 12 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=77, SST=88, summation (x_i-xbar)2=23,
summation (x_i-xbar)(y_i-ybar)=44.
Calculate the t test statistics to determine whether a
statistically linear relationship exists between x and y.
A sample of 7 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=24, SST=42
Using a 0.05 level of significance,...

One of the biggest changes in higher education in recent years
has been the growth of online universities. The Online Education
Database is an independent organization whose mission is to build a
comprehensive list of the top accredited online colleges. The
following table shows the retention rate (%) and the graduation
rate (%) for 29 online colleges. Retention Rate (%) Graduation Rate
(%) 7 25 51 25 4 28 29 32 33 33 47 33 63 34 45 36 60...

Shown below is a portion of an Excel output for regression
analysis relating Y (dependent variable) and X (independent
variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is the estimated regression equation
that relates Y to X?
2. Is the regression relationship significant?
Use the p-value approach and alpha = 0.05 to answer this
question.
3. What is the...

Shown below is a
portion of an Excel output for regression analysis relating Y
(dependent variable) and X (independent variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard
Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is
the estimated regression equation that relates Y to X? (2
Points)
2. Is the
regression relationship significant? Use the p-value approach and
alpha = 0.05 to answer this...

Kuya conducted a study to see if, among smokers, that there is a
significant difference in the sense of smoking urge between
individuals in various levels of administration. To
measure the urge to smoke, the Chronic Habit Obliging Killer
Emphysema (CHOKE) test was used. Type of profession was
categorized to Upper Management, Middle Management, and Lower
Management. The higher the score, the stronger the
urge. Is there a significant difference in their
urge?
UPPER
MIDDLE
LOWER
44
47
31
45
48
32
50
43...

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
model.
y= _____+...

A regression and correlation analysis resulted in the following
information regarding a dependent variable (y) and an
independent variable (x).
Σx = 90
Σ(y - )(x - ) = 466
Σy = 170
Σ(x - )2 = 234
n = 10
Σ(y - )2 = 1434
SSE = 505.98
The least squares estimate of the intercept or
b0 equals
Question 18 options:
a)
-1.991.
b)
.923.
c)
-.923.
d)
1.991.

Find the regression equation, letting the first variable be the
predictor (x) variable. Using the listed actress/actor ages in
various years, find the best predicted age of the Best Actor
winner given that the age of the Best Actress winner that year is
30 years. Is the result within 5 years of the actual Best Actor
winner, whose age was 48 years?
Best Actress
28
30
29
62
32
35
43
30
62
22
44
53
Best Actor
42
36...

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