Annual high temperatures in a certain location have been tracked for a sample of 7 years. Let XX represent the year and YY the high temperature (in C∘C∘). x y 5 32.08 6 30.15 7 28.62 8 22.89 9 24.76 10 20.43 11 19.8 Calculate the correlation coefficient. (Round to three decimal places.) r=r= Let's test the significance of the correlation coefficient at α=0.05α=0.05 significance level. H0:H0: There is not a significant relationship between the year and high temperature, i.e., ρ=0ρ=0. Ha:Ha: There is a significant relationship between the year and high temperature, i.e., ρ≠0ρ≠0. Calculate the test statistic. Round to three decimal places. t= Calculate the pp-value. Round to four decimal places. p-value =
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.
Annual high temperatures in a certain location have been tracked for a sample of 7 years. Let XX represent the year and YY the high temperature (in C∘C∘).
| x | y |
|---|---|
| 5 | 32.08 |
| 6 | 30.15 |
| 7 | 28.62 |
| 8 | 22.89 |
| 9 | 24.76 |
| 10 | 20.43 |
| 11 | 19.8 |
Calculate the
r=r=
Let's test the significance of the correlation coefficient at α=0.05α=0.05 significance level.
H0:H0: There is not a significant relationship between the year and high temperature, i.e., ρ=0ρ=0.
Ha:Ha: There is a significant relationship between the year and high temperature, i.e., ρ≠0ρ≠0.
- Calculate the test statistic. Round to three decimal places.
t= - Calculate the pp-value. Round to four decimal places.
p-value =
Given - The value of x and y
=56 n=7 = 178.73 , =1369.7 =476 ,=4703.688
To Find 1) Correlation coefficient
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