Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size—that is, the total time to produce a certain quantity of the product. Suppose she has collected data in the following table on the total time (in minutes) to produce 30 different orders of various quantities. Quantity Total Time (minutes) 105 172 125 189 135 221 141 323 149 248 171 317 190 372 204 185 206 250 240 177 255 397 277 227 299 228 335 369 371 490 Quantity Total Time (minutes) 388 351 392 428 400 412 421 545 439 443 439 320 455 587 458 483 480 513 486 423 493 403 506 700 586 593 589 456 665 643 #1) Develop the estimated regression equation. (Let x = quantity, and let y = total time (in minutes). Round your numerical values to four decimal places.) #2) Find the value of the test statistic. (Round your answer to two decimal places.) #3) Did the estimated regression equation provide a good fit? (Round your numerical answer to four decimal places.) Since r2 =
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.
| Quantity | Total Time (minutes) |
|---|---|
| 105 | 172 |
| 125 | 189 |
| 135 | 221 |
| 141 | 323 |
| 149 | 248 |
| 171 | 317 |
| 190 | 372 |
| 204 | 185 |
| 206 | 250 |
| 240 | 177 |
| 255 | 397 |
| 277 | 227 |
| 299 | 228 |
| 335 | 369 |
| 371 | 490 |
| Quantity | Total Time (minutes) |
|---|---|
| 388 | 351 |
| 392 | 428 |
| 400 | 412 |
| 421 | 545 |
| 439 | 443 |
| 439 | 320 |
| 455 | 587 |
| 458 | 483 |
| 480 | 513 |
| 486 | 423 |
| 493 | 403 |
| 506 | 700 |
| 586 | 593 |
| 589 | 456 |
| 665 |
643 |
#1) Develop the estimated regression equation. (Let x = quantity, and let y = total time (in minutes). Round your numerical values to four decimal places.)
#2) Find the value of the test statistic. (Round your answer to two decimal places.)
#3) Did the estimated regression equation provide a good fit? (Round your numerical answer to four decimal places.) Since r2 =
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