Extending the Concepts and SkillsMargin of Error in Regression. In Exercises and, you will examine the magnitude of the margin of error of confidence intervals and prediction intervals in regression as a function of how far the specified value of the predictor variable is from the mean of the observed values of the predictor variable.Age and Price of Orions. Refer to the data on age and price of a sample of 11 Orions given in Table on page 679.a. For each age between 2 and 7 years, obtain a 95% confidence interval for the mean price of all Orions of that age. Plot the confidence intervals against age and discuss your results.b. Determine the margin of error for each confidence interval that you obtained in part (a). Plot the margins of error against age and discuss your results.c. Repeat parts (a) and (b) for prediction intervals.TABLE Age and price data for a sample of 11 Orions Age(yr) x Price($100) y 5 85 4 103 6 70 5 82 5 89 5 98 6 66 6 95 2 169 7 70 7 48
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.
Extending the Concepts and Skills
Margin of Error in Regression. In Exercises and, you will examine the magnitude of the margin of error of confidence intervals and prediction intervals in regression as a
Age and Price of Orions. Refer to the data on age and price of a sample of 11 Orions given in Table on page 679.
a. For each age between 2 and 7 years, obtain a 95% confidence interval for the mean price of all Orions of that age. Plot the confidence intervals against age and discuss your results.
b. Determine the margin of error for each confidence interval that you obtained in part (a). Plot the margins of error against age and discuss your results.
c. Repeat parts (a) and (b) for prediction intervals.
TABLE Age and price data for a sample of 11 Orions
| Age(yr) x | Price($100) y |
| 5 | 85 |
| 4 | 103 |
| 6 | 70 |
| 5 | 82 |
| 5 | 89 |
| 5 | 98 |
| 6 | 66 |
| 6 | 95 |
| 2 | 169 |
| 7 | 70 |
| 7 | 48 |
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