Armer Company is accumulating data to use in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested the use of linear regression to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis follow: Month Maintenance Cost Machine Hours Jan.
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.
Armer Company is accumulating data to use in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested the use of linear regression to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the
| Month | Maintenance Cost | Machine Hours | ||||
| Jan. | $ | 5,050 | 820 | |||
| Feb. | 3,850 | 660 | ||||
| Mar. | 4,450 | 740 | ||||
| Apr. | 3,670 | 640 | ||||
| May | 5,200 | 840 | ||||
| June | 3,810 | 650 | ||||
| July | 3,880 | 660 | ||||
| Aug. | 5,320 | 940 | ||||
| Sept. | 5,110 | 830 | ||||
| Oct. | 4,900 | 810 | ||||
| Nov. | 4,150 | 690 | ||||
| Dec. | 4,010 | 680 | ||||
| Sum | $ | 53,400 | 8,960 | |||
| Average | $ | 4,450 | $ | 747 | ||
| Average cost per hour | $ | 6.00 | ||||
| a (intercept) | $ | 194.33 | ||||
| b (coefficient) | 6.2201 | |||||
| Standard error of the estimate | 144.247 | |||||
| R-squared | 0.9517 | |||||
| t-value for b | 14.030 | |||||
The coefficient of determination for Armer's regression equation for the maintenance activities is
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