Production Volume (units) Total Cost ($) 100 1730 200 2792 300 4129 400 5385 500 6497 600 7764 700 8835 800 10180 900 11412 Which of the following is your estimated regression equation? Total Cost = 468 + 12.1(Production Volume) + e Production Volume = 468 + 12.1(Total Cost) + e Total Cost = 468(Production Volume) + 12.1 + e Production Volume = 468(Total Cost) + 12.1 + e Will you reject the null hypothesis that the slope is zero at a significance level of 1%? Yes No Not enough information What is the R-square from your regression analysis? (Round your answer to four decimal places.) Which of the following is the correct interpretation of the R-square? Production volume explains 99.96% of the variation in total cost. Total cost explains 99.96% of the variation in production volume. The dependent variable explains 99.96% of the variation in the independent variable. 96% of the data points are on the estimated regression line. What is the estimated cost of producing 1000 radio units based on your estimated regression equation? (Round to the nearest whole number.) What is the estimated error term ("the residual") associated with production of 500 radio units? (Round to the nearest whole number.) What is the margin of error for a 95% confidence interval for the estimated total cost when production is 1000 radio units? (Round to one decimal place.) What is the margin of error for a 95% prediction interval for the estimated total cost when production is 1000 radio units? (Round to one decimal place.) Which of the following is a proper interpretation of your estimated slope? When production volume increases by one unit, total cost increases by $12.10 on average. When total costs increases by one dollar, production volume increases by $12.10 units on average. When production volume increases by one unit, total cost increases by $468 on average. When total costs increases by one dollar, production volume increases by 468 units on average. About how much of the variation in total costs cannot be explained by production volume? Less than 1% 1% 2% 3%
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Production Volume (units) |
Total Cost ($) |
100 |
1730 |
200 |
2792 |
300 |
4129 |
400 |
5385 |
500 |
6497 |
600 |
7764 |
700 |
8835 |
800 |
10180 |
900 |
11412 |
- Which of the following is your estimated regression equation?
- Total Cost = 468 + 12.1(Production Volume) + e
- Production Volume = 468 + 12.1(Total Cost) + e
- Total Cost = 468(Production Volume) + 12.1 + e
- Production Volume = 468(Total Cost) + 12.1 + e
- Will you reject the null hypothesis that the slope is zero at a significance level of 1%?
- Yes
- No
- Not enough information
- What is the R-square from your
regression analysis ? (Round your answer to four decimal places.) - Which of the following is the correct interpretation of the R-square?
- Production volume explains 99.96% of the variation in total cost.
- Total cost explains 99.96% of the variation in production volume.
- The dependent variable explains 99.96% of the variation in the independent variable.
- 96% of the data points are on the estimated regression line.
- What is the estimated cost of producing 1000 radio units based on your estimated regression equation? (Round to the nearest whole number.)
- What is the estimated error term ("the residual") associated with production of 500 radio units? (Round to the nearest whole number.)
- What is the margin of error for a 95% confidence interval for the estimated total cost when production is 1000 radio units? (Round to one decimal place.)
- What is the margin of error for a 95% prediction interval for the estimated total cost when production is 1000 radio units? (Round to one decimal place.)
- Which of the following is a proper interpretation of your estimated slope?
- When production volume increases by one unit, total cost increases by $12.10 on average.
- When total costs increases by one dollar, production volume increases by $12.10 units on average.
- When production volume increases by one unit, total cost increases by $468 on average.
- When total costs increases by one dollar, production volume increases by 468 units on average.
- About how much of the variation in total costs cannot be explained by production volume?
- Less than 1%
- 1%
- 2%
- 3%
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