Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow: Month Machine Hours Electricity Costs January 2,000 $ 18,950 February 2,400 $ 22,100 March 1,400 $ 14,050 April 2,600 $ 24,100 May 3,300 $ 28,800 June 2,800 $ 23,100 July 3,600 $ 25,300 August 3,000 $ 23,300 September 1,500 $ 16,600 October 3,200 $ 27,100 November 4,200 $ 32,100 December 3,700 $ 28,300 Summary Output Regression Statistics Multiple R 0.960 R Square 0.921 Adjusted R2 0.913 Standard Error 1,545.17 Observations 12.00 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7,465.99 1,566.61 4.77 0.00 3,975.37 10,956.62 Machine Hours 5.76 0.53 10.78 0.00 4.57 6.95 If the controller uses regression analysis to estimate costs, the estimate of the fixed portion of electricity costs is:
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.
Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:
| Month | Machine Hours | Electricity Costs | ||
| January | 2,000 | $ | 18,950 | |
| February | 2,400 | $ | 22,100 | |
| March | 1,400 | $ | 14,050 | |
| April | 2,600 | $ | 24,100 | |
| May | 3,300 | $ | 28,800 | |
| June | 2,800 | $ | 23,100 | |
| July | 3,600 | $ | 25,300 | |
| August | 3,000 | $ | 23,300 | |
| September | 1,500 | $ | 16,600 | |
| October | 3,200 | $ | 27,100 | |
| November | 4,200 | $ | 32,100 | |
| December | 3,700 | $ | 28,300 | |
| Summary Output | |
| Regression Statistics | |
| Multiple R | 0.960 |
| R Square | 0.921 |
| Adjusted R2 | 0.913 |
| Standard Error | 1,545.17 |
| Observations | 12.00 |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 7,465.99 | 1,566.61 | 4.77 | 0.00 | 3,975.37 | 10,956.62 |
| Machine Hours | 5.76 | 0.53 | 10.78 | 0.00 | 4.57 | 6.95 |
If the controller uses regression analysis to estimate costs, the estimate of the fixed portion of electricity costs is:
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