The data given in the following table shows equivalent temperatures on the Celsius temperature scale and the Fahrenheit temperature scale. (A graphing calculator is recommended. Round your answers to two decimal places.) Celsius (x°) −40 0 100 Fahrenheit (y°) −40 32 212 (a) Find the linear correlation coefficient for the data. (b) What is the significance of the value found in part (a)? The value in part (a) is insignificant.The value in part (a) is a perpendicular line. The data displays a perfect linear relationship.The data displays a quadratic relationship.The correlation obtained by the data is not linear. (c) Find the equation of the least-squares regression line. ŷ = (d) Use the equation of the least-squares line from part (c) to predict the Fahrenheit temperature that corresponds to a Celsius temperature of 15°. °F (e) Is the procedure in part (d) an example of interpolation or extrapolation? interpolationextrapolation
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.
The data given in the following table shows equivalent temperatures on the Celsius temperature scale and the Fahrenheit temperature scale. (A graphing calculator is recommended. Round your answers to two decimal places.)
| Celsius (x°) | −40 0 100 |
|---|---|
| Fahrenheit (y°) | −40 32 212 |
(b) What is the significance of the value found in part (a)?
(c) Find the equation of the least-squares regression line.
ŷ =
(d) Use the equation of the least-squares line from part (c) to predict the Fahrenheit temperature that corresponds to a Celsius temperature of 15°.
°F
(e) Is the procedure in part (d) an example of interpolation or extrapolation?
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