Tobias Ali

2021-01-28

A linear regression was performed on a bivariate data set with variables x and y. Analysis by a computer software package included the following outputs:
Sample Size: $n=15$
Regression Equation: $y\stackrel{^}{e}=0.359-1.264x$
Coefficient of Determination: r square = 0.915
Sums of Squares :$SSy=35.617.SSex=32.589,SSresid=3.028$
a. Calculate the standard error Se.
b. write a sentence interpreting the value of rsquare.
c.What is the value of Pearsons

### Answer & Explanation

smallq9

Step 1
Note: Since in this question there are 4 parts, but we are authorized to answer only up to three parts, as you have not mentioned which parts you need so we are doing First three parts.
In this question, is has been given,
Sample Size: $n=15$
Regression Equation: $y\stackrel{^}{e}=0.359-1.264x$
Coefficient of Determination: r square = 0.915
Sums of Squares :$SSy=35.617.SSx=32.589,SSresidual=3.028$
Using this we have to find the value of Standard error, Correlation Coefficient and explain the value of r squared.
Step 2
Part A)
The calculations of Standard error has shown below,
Standard error = 8.71
$SE=SS\frac{E}{\sqrt{n-1}}=\frac{SSy-SSresidual}{\sqrt{n-1}}$
$SE=\frac{35.617-3.028}{\sqrt{15-1}}$
$Se=8.71$
Step 3
Part b)
The coefficient of determination interprets that how well your observed variables can be explained by model, For, e.g. If Coefficient of determination is having the value of 0.50, which means half of the total observed values can be explained by model.
We have the value of R square, which is 0.915, which means $91.5\mathrm{%}$ of your observed values can be explained by the model.
Step 4
Part C)
We have the value of r- squared and we have to find the value of Correlation coeffcient(r) , to get this value we need to to square root of r-squared value.
$r=0.96$
Pearson's Correlation Coefficient $=r=\sqrt{{r}^{2}}=\sqrt{0.915}=0.96$

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