Biologists have found that there is a relationship between the rate of a cricket’s chirp and the temperature. A regression model is determined, with the predictor variable x=x= chirps per second and the response variable y=y= temperature (°F). The data on which the model is based is given below, along with output of the regression analyis. Chirps 13 16 16 17 18 19 19 20 20 23 Temperature 68.4 78.4 71.2 72.5 74 84.2 87.1 80 83 91.1 Correlation Coefficient: r=r= 0.865 Least Squares Equation: ˆy=36.93+2.32xy^=36.93+2.32x a. Use the given regression line equation to predict the temperature (round to 1 decimal place) if the rate of cricket chirps is: 14 chirp/sec, predicted temp== °F 27 chirp/sec, predicted temp== °F b. Is one of these predictions more reliable than the other? The prediction corresponding to 27 chirps/sec is more reliable. The prediction corresponding to 14 chirps/sec is more reliable. Both predictions are equally reliable since they are based on the same regression model. c. Based on the linear regression model, what percentage of the variation in xx can be explained by the corresponding variation in yy? 2.32 % 93 % 36.93 % 86.5 % 74.8 %
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.
Biologists have found that there is a relationship between the rate of a cricket’s chirp and the temperature. A regression model is determined, with the predictor variable x=x= chirps per second and the response variable y=y= temperature (°F). The data on which the model is based is given below, along with output of the regression analyis.
| Chirps | 13 | 16 | 16 | 17 | 18 | 19 | 19 | 20 | 20 | 23 |
|---|---|---|---|---|---|---|---|---|---|---|
| Temperature | 68.4 | 78.4 | 71.2 | 72.5 | 74 | 84.2 | 87.1 | 80 | 83 | 91.1 |
| r=r= 0.865 | |
| Least Squares Equation: | ˆy=36.93+2.32xy^=36.93+2.32x |
a. Use the given regression line equation to predict the temperature (round to 1 decimal place) if the rate of cricket chirps is:
- 14 chirp/sec, predicted temp== °F
- 27 chirp/sec, predicted temp== °F
b. Is one of these predictions more reliable than the other?
- The prediction corresponding to 27 chirps/sec is more reliable.
- The prediction corresponding to 14 chirps/sec is more reliable.
- Both predictions are equally reliable since they are based on the same regression model.
c. Based on the linear regression model, what percentage of the variation in xx can be explained by the corresponding variation in yy?
- 2.32 %
- 93 %
- 36.93 %
- 86.5 %
- 74.8 %
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
