The manager of a billing department of a large family practice would like to dev
ID: 3157206 • Letter: T
Question
The manager of a billing department of a large family practice would like to develop a model to predict the amount of time it takes to process invoices. Data are collected from a sample of thirty days with the following results:
column 1, day 1-30; column 2 invoices processed x; 149; 60, 188; 19; 201; 58; 77; 222; 181; 30; 110; 83; 60; 25; 173; 169; 190; 233; 289; 45; 193; 70; 241; 103; 163; 120; 201; 135; 80; 29; column 3 completion time in hours y; 2.1; 1.8; 2.3; 0.3; 2.7; 1.0; 1.7; 3.1; 2.8; 1.0; 1.5; 1.2; 0.8; 0.4; 2.0; 2.5; 2.9; 3.4; 4.1; 1.2; 2.5; 1.8; 3.8; 1.5; 2.8; 2.5; 3.3; 2.0; 1.7; 0.5
Find the regression equation describing the linear relationship between the two variables
Compute r2 and provide an interpretation.
Construct an ANOVA table and Test with an F test. Let = .05.
Test with a t test. Let = .05.
Demonstrate the equivalence of the tests in c. and d.
Please note: I have most of the spread sheet completed but want to double check my answers and having problems with the data analysis, regression
Explanation / Answer
The regression model is given as below:
Simple Linear Regression Analysis
Regression Statistics
Multiple R
0.9447
R Square
0.8924
Adjusted R Square
0.8886
Standard Error
0.3342
Observations
30
ANOVA
df
SS
MS
F
Significance F
Regression
1
25.9438
25.9438
232.2200
0.0000
Residual
28
3.1282
0.1117
Total
29
29.0720
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
0.4024
0.1236
3.2559
0.0030
0.1492
0.6555
Invoice processed
0.0126
0.0008
15.2388
0.0000
0.0109
0.0143
The correlation coefficient between two variables invoice processed and completion time in hours is given as 0.9447 which means there is a high positive or strong linear relationship or association or correlation exists between the given two variables. The coefficient of determination or the value of the R square is given as 0.8924 which means about 89.24% of the variation in the dependent variable completion time in hours is explained by the independent variable number of invoices processed.
The p-value for this ANOVA is given as 0.00 which is less than the given level of significance or alpha value 0.05 so we reject the null hypothesis that there is no any significant relationship exists between the given two variables invoice processed and completion time in hours.
Simple Linear Regression Analysis
Regression Statistics
Multiple R
0.9447
R Square
0.8924
Adjusted R Square
0.8886
Standard Error
0.3342
Observations
30
ANOVA
df
SS
MS
F
Significance F
Regression
1
25.9438
25.9438
232.2200
0.0000
Residual
28
3.1282
0.1117
Total
29
29.0720
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
0.4024
0.1236
3.2559
0.0030
0.1492
0.6555
Invoice processed
0.0126
0.0008
15.2388
0.0000
0.0109
0.0143
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