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=15Regression Equation: y hate =0.359 - 1.264xCoefficient of Determination: r square = 0.915Sums of Squares :SSy = 35.617. SSex = 32.589, SSresid = 3.028a. Calculate the standard error Se.b. write a sentence interpreting the value of rsquare.c.What is the value of Pearson's correlation coefficient?d. Determine whether the variables x and y are significant using a 5% significance level. You may assume a simple random sample from a bivariate normal populaton.

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Asked Jun 19, 2019
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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 hate =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 Pearson's correlation coefficient?

d. Determine whether the variables x and y are significant using a 5% significance level. You may assume a simple random sample from a bivariate normal populaton.

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Expert Answer

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 hate = 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

 

SSy SSresidual
SSE
SE
Уп-1
Vn-1
35.617-3.028
SE
V15-1
SE = 8.71
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SSy SSresidual SSE SE Уп-1 Vn-1 35.617-3.028 SE V15-1 SE = 8.71

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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 hav...

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