An important application of regression analysis is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, one can estimate the cost associated with a particular manufacturing volume. Consider the following sample of monthly production volumes and total costs data for a manufacturing operation for the year 2018. Month (Year 2018) Production Volume (units) Total Costs ($) January 500 6,000 February 350 4,000 March 450 5,000 April 550 5,400 May 600 5.900 June 400 4,000 July 400 4,200 August 350 3,900 September 400 4,300 October 600 6,000 November 700 6,400 December 750 7,000 3. Which of the following is NOT necessarily true about the interpretation of the value of b in the simple linear regression equation y = a + bx for this problem? I. The monthly total costs will increase by $7.6437 for every one-unit increase in the production volume. II. Since b > 0, there is a direct relationship between production volume and total costs. III. Because b > 1, there is a very strong positive linear relationship between production volume and total costs. A. i and ii only B. ii only C. iii only D. ii and iii only 4. Which of the following statements are true about the dependent (or response) and independent (or predictor) variables for the simple linear model in this problem? I. Production volume is dependent on total costs. II. The predictor and response variables are the production volume and total costs, respectively. III. The total costs can be projected using the simple linear regression equation if the production volume is known. A. i and ii only B. i and iii only C. ii and iii only D. i, ii, and iii 5. Calculate the (Pearson) correlation coefficient between production volume and total costs in this problem. A. 0.8391 B. 0.9571 C. 0.9160 D. 0.9783
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.
FOR 3-8: An important application of
| Month (Year 2018) | Production Volume (units) | Total Costs ($) |
| January | 500 | 6,000 |
| February | 350 | 4,000 |
| March | 450 |
5,000 |
| April | 550 | 5,400 |
| May | 600 | 5.900 |
| June | 400 | 4,000 |
| July | 400 | 4,200 |
| August | 350 | 3,900 |
| September | 400 | 4,300 |
| October | 600 | 6,000 |
| November | 700 | 6,400 |
| December | 750 | 7,000 |
3. Which of the following is NOT necessarily true about the interpretation of the value of b in the simple linear regression equation y = a + bx for this problem?
I. The monthly total costs will increase by $7.6437 for every one-unit increase in the production volume.
II. Since b > 0, there is a direct relationship between production volume and total costs.
III. Because b > 1, there is a very strong positive linear relationship between production volume and total costs.
A. i and ii only
B. ii only
C. iii only
D. ii and iii only
4. Which of the following statements are true about the dependent (or response) and independent (or predictor) variables for the simple linear model in this problem?
I. Production volume is dependent on total costs.
II. The predictor and response variables are the production volume and total costs, respectively.
III. The total costs can be projected using the simple linear regression equation if the production volume is known.
A. i and ii only
B. i and iii only
C. ii and iii only
D. i, ii, and iii
5. Calculate the (Pearson)
A. 0.8391
B. 0.9571
C. 0.9160
D. 0.9783
6. Which of the following is the most suitable interpretation of the (Pearson) correlation coefficient between production volume and total costs in this problem?
A. There is a perfect
B. There is a very strong positive correlation between production volume and total costs.
C. There is a strong positive correlation between production volume and total costs.
D. There is a positive correlation between production volume and total costs.
7. The equation of the regression line is given by
A. ? = −116.01 + 0.12?
B. ? = 1321.32 − 7.64?
C. ? = 116.01 + 0.12?
D. ? = 7.64? + 1321.32
8. How much is the estimated total costs if the corresponding production volume for a particular month is 300 units?
A. $274.80
B. $287.13
C. $2,293.11
D. $3,614.43
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