Consider the data set below. x 8 9 8 2 9 7 y 8 1 1 1 8 2 For a hypothesis test, where H0:β1=0 and H1:β1≠0, and using α=0.01, give the following: (a) The test statistic t= (b) The degree of freedom df= (c) The rejection region |t|> _____ The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that β1=0.
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.
Consider the data set below.
| x | 8 | 9 | 8 | 2 | 9 | 7 |
| y | 8 | 1 | 1 | 1 | 8 | 2 |
For a hypothesis test, where H0:β1=0 and H1:β1≠0, and using α=0.01, give the following:
(a) The test statistic
t=
(b) The degree of freedom
df=
(c) The rejection region
|t|> _____
The final conclustion is
A. There is not sufficient evidence to reject the null hypothesis that β1=0.
B. We can reject the null hypothesis that β1=0 and accept that β1≠0.
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