The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time it takes to process invoices. Data are collected from a sample of 30 days with the following results: Relating time to invoices processed. Day Invoices Processed Completion Time (hours) Day Invoices Processed Completion Time (hours) 1 149 2.1 16 169 2.5 2 60 1.8 17 190 2.9 3 188 2.3 18 233 3.4 4 19 0.3 19 289 4.1 5 201 2.7 20 45 1.2 6 58 1.0 21 193 2.5 7 77 1.7 22 70 1.8 8 222 3.1 23 241 3.8 9 181 2.8 24 103 1.5 10 30 1.0 25 163 2.8 11 110 1.5 26 120 2.5 12 83 1.2 27 201 3.3 13 60 0.8 28 135 2.0 14 25 0.4 29 80 1.7 15 173 2.0 30 29 0.5 Hint: Determine which are the independent and dependent variables. Set up a scatter diagram. Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1. Interpret the meaning of the Y intercept b0 and the slope b1 in this problem. Use the regression model developed in the (b) to predict the average amount of time it would take to process 150 invoices. Compute the standard error of the estimate. Compute the coefficient of determination r2 and interpret its meaning. Compute the coefficient of correlation
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- The manager of the purchasing department of a large banking organization would like to develop a model to predict the amount of time it takes to process invoices. Data are collected from a sample of 30 days with the following results:
Relating time to invoices processed.
|
Day |
Invoices Processed |
Completion Time (hours) |
Day |
Invoices Processed |
Completion Time (hours) |
|
1 |
149 |
2.1 |
16 |
169 |
2.5 |
|
2 |
60 |
1.8 |
17 |
190 |
2.9 |
|
3 |
188 |
2.3 |
18 |
233 |
3.4 |
|
4 |
19 |
0.3 |
19 |
289 |
4.1 |
|
5 |
201 |
2.7 |
20 |
45 |
1.2 |
|
6 |
58 |
1.0 |
21 |
193 |
2.5 |
|
7 |
77 |
1.7 |
22 |
70 |
1.8 |
|
8 |
222 |
3.1 |
23 |
241 |
3.8 |
|
9 |
181 |
2.8 |
24 |
103 |
1.5 |
|
10 |
30 |
1.0 |
25 |
163 |
2.8 |
|
11 |
110 |
1.5 |
26 |
120 |
2.5 |
|
12 |
83 |
1.2 |
27 |
201 |
3.3 |
|
13 |
60 |
0.8 |
28 |
135 |
2.0 |
|
14 |
25 |
0.4 |
29 |
80 |
1.7 |
|
15 |
173 |
2.0 |
30 |
29 |
0.5 |
|
|
Hint: Determine which are the independent and dependent variables.
- Set up a
scatter diagram . - Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1.
- Interpret the meaning of the Y intercept b0 and the slope b1 in this problem.
- Use the regression model developed in the (b) to predict the average amount of time it would take to process 150 invoices.
- Compute the standard error of the estimate.
- Compute the coefficient of determination r2 and interpret its meaning.
- Compute the coefficient of
correlation r.
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