Answer the following problem based on the concept of Linear Correlation and Regression. Do not round off to the process of computing it but on the answers on this, round off your answers based on the instructions given. Use the formula of Pearson for computing the value of r. 1. A classic application of correlation involves the association between the temperature and the number of times a cricket chirps in 1 minute. Listed below are the number of chirps in 1 minute and the corresponding temperatures in degree Fahrenheit. Is there a significant evidence to conclude that there is a linear correlation between the number of chirps in 1 minute and the temperature? Use alpha = 0.01. (Show solution) Chirps in 1 minute (x) Temperature (y) 882 69.7 1188 93.3 1104 84.3 864 76.3 1200 88.6 1032 82.6 960 71.6 900 79.6 a. Based on the problem, What is the decision rule? Do not reject the null hypothesis. Reject the null hypothesis. b. Based on the problem, What is the conclusion? There is a significant linear relationship between the chirps in 1 minute and the temperature. There is no significant linear relationship between the chirps in 1 minute and the temperature. c. Based on the problem and solving for the regression line y_pred = mx + b, what is the value of m? [Round off to 4 decimal places.] If the answer is negative, make sure to also include the negative sign. d. Based on the problem and solving for the regression line y_pred = mx + b, what is the value of b? [Round off to 2 decimal places.] If the answer is negative, make sure to also include the negative sign.
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.
Answer the following problem based on the concept of Linear
Use the formula of Pearson for computing the value of r.
1. A classic application of correlation involves the association between the temperature and the number of times a cricket chirps in 1 minute. Listed below are the number of chirps in 1 minute and the corresponding temperatures in degree Fahrenheit. Is there a significant evidence to conclude that there is a linear correlation between the number of chirps in 1 minute and the temperature? Use alpha = 0.01. (Show solution)
| Chirps in 1 minute (x) | Temperature (y) |
| 882 | 69.7 |
| 1188 | 93.3 |
| 1104 | 84.3 |
| 864 | 76.3 |
| 1200 | 88.6 |
| 1032 | 82.6 |
| 960 | 71.6 |
| 900 | 79.6 |
a. Based on the problem, What is the decision rule?
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