Question

The standard error of the regression coefficient is .009. Calculate a statistical test to determine if the regression coefficient differs from 0. State the research and null hypothesis. What table value is needed to reject the null hypothesis? What is the value of your calculated test statistic? What is the approximate probability of making a Type I error? What do you conclude about the nature of the linear relationship between state population density and covid19 mortality rate?

Answer 1

Answer:-

Given That:-

The standard error of the regression coefficient is .009. Calculate a statistical test to determine if the regression coefficient differs from 0. State the research and null hypothesis. What table value is needed to reject the null hypothesis? What is the value of your calculated test statistic? What is the approximate probability of making a Type I error? What do you conclude about the nature of the linear relationship between state population density and covid19 mortality rate?

Given,

The Standard error of Regression coefficient is 0.009

I considered a simple Linear regression model

where n is the sample size.

Now fitted model is

Where

and   is the O.L.S estimater

Now we want to test,

verses

Test Statistic (t)

Put your regression coefficient value and you will get the test statistice.

Critical table value to reject H0:

which can be obtained from ttable with n - 2 degree of freedom and significance level  .

Here I don't know how many sample size are there, so dear please put your sample size as n, then degree of freedom is n - 2 take = 0.05. Now using a calculator or t table = 0.05 and d.f = n - 2.

Conclusion:

If t > , we reject H0 and conclude there is a linear relationship.

If t < , we can't reject H0 ,so we conclude there is no linear relationship.

Dear to answer this question precisely we need fitted regression equation. But here it is not given. But don't worry I will help you in your studies.. Follow my steps. If you have regression equation and Regression coefficient then put your value in the provided steps , finally you will get the answer..

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