The following observations are obtained from a random sample of 10 individuals: Individual x y 1 9.63 5.06 2 4.80 3.20 3 6.84 4.48 4 10.2 5.62 5 8.81 4.13 6 10.4 5.55 7 4.19 3.35 8 8.21 5.77 9 7.97 4.81 10 9.11 5.64 Run a t-linear regression test on this data. (HINT: make sure you copy the numbers correctly!) What are the appropriate null and alternative hypotheses? H0:r=0H1:r<0H0:r=0H1:r<0 H0:r=0H1:r≠0H0:r=0H1:r≠0 H0:ρ=0H1:ρ<0H0:ρ=0H1:ρ<0 H0:r=0H1:r>0H0:r=0H1:r>0 H0:ρ=0H1:ρ≠0H0:ρ=0H1:ρ≠0 H0:ρ=0H1:ρ>0H0:ρ=0H1:ρ>0 What is the correlation coefficient? Round to 4 decimals. What is the coefficient of determination? Round to 4 decimals.
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 following observations are obtained from a random sample of 10 individuals:
|
Individual |
x |
y |
|
1 |
9.63 |
5.06 |
|
2 |
4.80 |
3.20 |
|
3 |
6.84 |
4.48 |
|
4 |
10.2 |
5.62 |
|
5 |
8.81 |
4.13 |
|
6 |
10.4 |
5.55 |
|
7 |
4.19 |
3.35 |
|
8 |
8.21 |
5.77 |
|
9 |
7.97 |
4.81 |
|
10 |
9.11 |
5.64 |
Run a t-linear regression test on this data. (HINT: make sure you copy the numbers correctly!)
What are the appropriate null and alternative hypotheses?
|
H0:r=0H1:r<0H0:r=0H1:r<0 |
||
|
H0:r=0H1:r≠0H0:r=0H1:r≠0 |
||
|
H0:ρ=0H1:ρ<0H0:ρ=0H1:ρ<0 |
||
|
H0:r=0H1:r>0H0:r=0H1:r>0 |
||
|
H0:ρ=0H1:ρ≠0H0:ρ=0H1:ρ≠0 |
||
|
H0:ρ=0H1:ρ>0H0:ρ=0H1:ρ>0 |
What is the
What is the coefficient of determination? Round to 4 decimals.
Calculate the value of the test statistic. Round your response to at least 2 decimal places.
|t||t|=
What is the corresponding P-value for the test statistic? Round your response to at least 6 decimal places.
Make a decision (hint: when in doubt, use the α=.05α=.05 significance level)
Since αα >> PP, we Reject the null hypothesis H0H0
Help write a summary of the results of this hypothesis test:
There is enough evidence in this sample to conclude there is a correlation between the variables X and Y at the αα= .05 significance level because P=P= .
What is the equation of the Regression line? Round the values to 4 decimal places
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
