HCM 3001 Fall 2023 Class Exercises
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Humber College *
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Course
3001
Subject
Statistics
Date
Feb 20, 2024
Type
xlsx
Pages
11
Uploaded by SargentBook16495
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.60449274
R Square
0.36541148
Adjusted R S
0.290754
Standard Erro15.0194881
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
2 2208.25463 1104.12732 4.89450633 0.02094999
Residual
17 3834.94537 225.585022
Total
19
6043.2
CoefficientsStandard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Intercept
-30.5545893 17.9916466 -1.69826531 0.10768462 -68.5136456 7.40446695 -68.5136456
0.24659898 0.24583397 1.00311188
0.3298723 -0.27206537 0.76526333 -0.27206537
36.8256268
12.724272 2.89412446 0.01008738 9.97975957
63.671494 9.97975957
Medication Errors Case-Mix Index
# of Falls
Intercepts + (Medication Error *20) + (CMI*1.5)
y=a+ (b1*x1) + (b2*x2)
29.6158304
Upper 95.0%
7.40446695
0.76526333
63.671494
Example 5: Multiple Linear Regression
Using linear regression, what is the prediction for Falls at a hospital with 20 medication errors and a CMI of 1.5
Hospital
1
26
6
1.392
2
43
5
1.392
3
8
26
0.889
4
16
17
0.889
5
18
12
1.38
6
11
9
1.38
7
24
21
1.628
8
28
7
1.628
9
8
1
1.08
10
20
26
1.08
11
22
44
1.72
12
86
39
1.72
13
18
3
1.22
14
14
6
1.334
15
17
4
1.689
16
46
4
1.689
17
8
24
1.12
18
16
36
1.12
19
29
40
1.505
20
26
25
1.505
Patient Falls Medication Errors Case-Mix Index
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5?
Example 4: Linear Prediction of ED Visits
Using linear regression, what is the prediction for total ED visits in Year 6?
Year
ED Visits
1
16,067
2
15,194
3
13,844
4
12,779
5
10,813
6
?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.91081211
R Square
0.82957871
Adjusted R S
0.81253658
Standard Erro0.04141092
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
1 0.08347636 0.08347636 48.6781134 3.82037E-05
Residual
10 0.01714864 0.00171486
Total
11
0.100625
CoefficientsStandard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Intercept
0.06040655
0.0274101 2.20380646 0.05210426 -0.00066695 0.12148005 -0.00066695
0.01557642 0.00223255 6.97697021 3.82037E-05 0.01060199 0.02055084 0.01060199
Revenue in $M (x)
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b
a
profit
revenue
intercept
y=a+bx
y
10 0.06040655
0.21617072
Upper 95.0%
0.12148005
0.02055084
Example 3: Linear Regression
Using linear regression, what is the predicted profit for a clinic with $10M in revenues?
Private Cosmetic Surgery Clinic Revenues and Profits
Clinic
x*y
1
$7.10
$0.16
1.14
50.41
2
$2.02
$0.11
0.22
4.08
3
$6.06
$0.13
0.79
36.72
4
$4.01
$0.16
0.64
16.08
5
$14.09
$0.26
3.66
198.53
6
$15.09
$0.28
4.23
227.71
7
$16.02
$0.24
3.84
256.64
8
$12.03
$0.21
2.53
144.72
9
$14.00
$0.27
3.78
196.00
10
$20.01
$0.44
8.80
400.40
11
$15.09
$0.35
5.28
227.71
12
$7.06
$0.18
1.27
49.84
Total
$133
$2.79
36.18
1,808.84
Revenue in $M (x)
Profit in $M
(y)
x
2
$0.00
$0.00
$0.05
$0.10
$0.15
$0.20
$0.25
$0.30
$0.35
$0.40
$0.45
$0.50
1
$0.00
$5.00
$10.00
$15.00
$20.00
$25.00
$5.00
$10.00
$15.00
$20.00
$25.00
Profit in $M
(y)
1
2
3
4
5
6
7
8
9
10
11
12
Chart Title
Revenue in $M (x)
Profit in $M
(y)
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Example 2: Weighted Moving Average
Using a 3-period weighted moving average, what is the prediction for total ED visits in Year 6?
Period
Visits
Weights
1
16,067
0.0
0
2
15,194
0.0
0
3
13,844
0.10
1,384
4
12,779
0.30
3,834
5
10,813
0.60
6,488
6
12,478
1.00
11,706
3-period Moving Average
Prediction
3-period Weighted Moving Average
Prediction
Example 1: Moving Average
Using a 3-period moving average, what is the prediction for total ED visits in Year 6?
Formula 1
Formula 2
Year
ED Visits
1
16,067
2
15,194
3
13,844
4
12,779
5
10,813
6
?
12,478
12,478
3-period Moving Average Prediction
3-period Moving Average Prediction
Related Documents
Related Questions
**Please complete table**
arrow_forward
What is the value of the Coefficient of Determination (Adjusted for Degrees of Freedom) ? (four decimal places, +/- 0.0050)
arrow_forward
A multiple regression analysis produced the following tables.
Summary Output
Regression Statistics
Multiple R
0.978724022
R Square
0.957900711
Adjusted R Square
0.952287472
Standard Error
67.67055418
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
2
1562918.941
781459.5
170.6503
4.80907E-11
Residual
15
68689.55855
4579.304
Total
17
1631608.5
Coefficients
Standard Error
t Stat
P-value
Intercept
1959.709718
306.4905312
6.39403
1.21E-05
X1
-0.469657287
0.264557168
-1.77526
0.096144
X2
-2.163344882
0.278361425
-7.77171
1.23E-06
The regression equation for…
arrow_forward
A multiple regression analysis produced the following tables.
Summary Output
Regression Statistics
Multiple R
0.978724022
R Square
0.957900711
Adjusted R Square
0.952287472
Standard Error
67.67055418
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
2
1562918.941
781459.5
170.6503
4.80907E-11
Residual
15
68689.55855
4579.304
Total
17
1631608.5
Coefficients
Standard Error
t Stat
P-value
Intercept
1959.709718
306.4905312
6.39403
1.21E-05
X1
-0.469657287
0.264557168
-1.77526
0.096144
X2
-2.163344882
0.278361425
-7.77171
1.23E-06
Using α = 0.01 to test the…
arrow_forward
A multiple regression analysis produced the following tables.
Summary Output
Regression Statistics
Multiple R
0.978724022
R Square
0.957900711
Adjusted R Square
0.952287472
Standard Error
67.67055418
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
2
1562918.941
781459.5
170.6503
4.80907E-11
Residual
15
68689.55855
4579.304
Total
17
1631608.5
Coefficients
Standard Error
t Stat
P-value
Intercept
1959.709718
306.4905312
6.39403
1.21E-05
X1
-0.469657287
0.264557168
-1.77526
0.096144
X2
-2.163344882
0.278361425
-7.77171
1.23E-06
For x1= 360 and x2 = 220, the…
arrow_forward
A multiple regression analysis produced the following tables.
Summary Output
Regression Statistics
Multiple R
0.978724022
R Square
0.957900711
Adjusted R Square
0.952287472
Standard Error
67.67055418
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
2
1562918.941
781459.5
170.6503
4.80907E-11
Residual
15
68689.55855
4579.304
Total
17
1631608.5
Coefficients
Standard Error
t Stat
P-value
Intercept
1959.709718
306.4905312
6.39403
1.21E-05
X1
-0.469657287
0.264557168
-1.77526
0.096144
X2
-2.163344882
0.278361425
-7.77171
1.23E-06
Using α = 0.01 to test the…
arrow_forward
A multiple regression analysis produced the following tables.
Summary Output
Regression Statistics
Multiple R
0.978724022
R Square
0.957900711
Adjusted R Square
0.952287472
Standard Error
67.67055418
Observations
18
ANOVA
df
SS
MS
F
Significance F
Regression
2
1562918.941
781459.5
170.6503
4.80907E-11
Residual
15
68689.55855
4579.304
Total
17
1631608.5
Coefficients
Standard Error
t Stat
P-value
Intercept
1959.709718
306.4905312
6.39403
1.21E-05
X1
-0.469657287
0.264557168
-1.77526
0.096144
X2
-2.163344882
0.278361425
-7.77171
1.23E-06
These results indicate that…
arrow_forward
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
1
3390.0
3390.0
19.4
0.000
Residual Error
174
30397.8
174.7
Total
175
33787.8
Use the information in the table to give the sample size and to calculate R^2.Enter the exact answer for the sample size, and round R^2 to one decimal place.Enter your answer; n Enter your answer; R^2 %
arrow_forward
Source of variation
Due to regression (ESS)
Due to residual (RSS)
Total (TSS)
Sum of squares
(SS)
65,965
66,042
d.f.
and
||
14
Mean sum of
squares (MSS)
a. What is the sample size?
b. What is the value of the RSS?
c. What are the d.f. of the ESS and RSS?
d. What is R²?
And adjusted R²?_
e. What is the F-score in the test of the hypothesis that X2 and X3 have zero influence on Y.
f. From the preceding information, can you determine the individual contribution of X2 and X3
toward Y?
arrow_forward
Please Fast carect answers
arrow_forward
WALKING
RUNNING
Mean
7.181818182
7.3636364
Variance
4.563636364
6.4545455
Observations
11
11
Pooled Variance
5.509090909
Hypothesized Mean Difference
0
df
20
t Stat
-0.181668105
P(T<=t) one-tail
0.428835886
t Critical one-tail
1.724718243
P(T<=t) two-tail
0.857671772
t Critical two-tail
2.085963447
If the t-Stat value is less than the t Critical two-tail value I can reject the null, right? I am still a little confused on what a few numbers represent.
arrow_forward
Refer to the ANOVA table for this regression.
Source
SS
d.f.
MS
Regression
1,164,578
5
232,916
Residual
1,500,689
45
33,349
Total
2,665,267
50
(a) State the degrees of freedom for the F test for overall significance.
arrow_forward
Comparison of mean reading test scores by ethnic background (Caucasian, African American, Hispanic, & Asian).
A. T-test dependent samples
B. One-way ANOVA
C. Correlation
D. Chi square
E. Simple Regression
arrow_forward
For a data analysis what is the conclusion supported by the ANOVA Table.
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
53.86111
3
17.9537
3.570902
0.02465
2.90112
Within Groups
160.8889
32
5.027778
Total
214.75
35
arrow_forward
Use the following ANOVA table for regression to answer the questions.
Response: Y
Source
DF
Sum Sq
Mean Sq
F-value
Pr(>F)
Regression
1
351.94
351.94
12.73
0.000
Residual Error
359
9926.35
27.65
Total
360
10278.29
Give the F-statistic and p-value.The F-statistic is The p-value is
Choose the conclusion of this test using a 5%5% significance level.
A) Reject H0H0. The model is not effective.
B) Reject H0H0. The model is effective.
C) Do not reject H0H0. We did not find evidence that the model is not effective.
D) Do not reject H0H0. We did not find evidence that the model is effective.
arrow_forward
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Related Questions
- **Please complete table**arrow_forwardWhat is the value of the Coefficient of Determination (Adjusted for Degrees of Freedom) ? (four decimal places, +/- 0.0050)arrow_forwardA multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 The regression equation for…arrow_forward
- A multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 Using α = 0.01 to test the…arrow_forwardA multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 For x1= 360 and x2 = 220, the…arrow_forwardA multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 Using α = 0.01 to test the…arrow_forward
- A multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 These results indicate that…arrow_forwardAnalysis of Variance Source DF SS MS F P Regression 1 3390.0 3390.0 19.4 0.000 Residual Error 174 30397.8 174.7 Total 175 33787.8 Use the information in the table to give the sample size and to calculate R^2.Enter the exact answer for the sample size, and round R^2 to one decimal place.Enter your answer; n Enter your answer; R^2 %arrow_forwardSource of variation Due to regression (ESS) Due to residual (RSS) Total (TSS) Sum of squares (SS) 65,965 66,042 d.f. and || 14 Mean sum of squares (MSS) a. What is the sample size? b. What is the value of the RSS? c. What are the d.f. of the ESS and RSS? d. What is R²? And adjusted R²?_ e. What is the F-score in the test of the hypothesis that X2 and X3 have zero influence on Y. f. From the preceding information, can you determine the individual contribution of X2 and X3 toward Y?arrow_forward
- Please Fast carect answersarrow_forwardWALKING RUNNING Mean 7.181818182 7.3636364 Variance 4.563636364 6.4545455 Observations 11 11 Pooled Variance 5.509090909 Hypothesized Mean Difference 0 df 20 t Stat -0.181668105 P(T<=t) one-tail 0.428835886 t Critical one-tail 1.724718243 P(T<=t) two-tail 0.857671772 t Critical two-tail 2.085963447 If the t-Stat value is less than the t Critical two-tail value I can reject the null, right? I am still a little confused on what a few numbers represent.arrow_forwardRefer to the ANOVA table for this regression. Source SS d.f. MS Regression 1,164,578 5 232,916 Residual 1,500,689 45 33,349 Total 2,665,267 50 (a) State the degrees of freedom for the F test for overall significance.arrow_forward
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