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There have 7 Regression Modelling final exam practice questions. In the "My own solutions. docx" I have finished question 1,2,3,5 and some of...

There have 7 Regression Modelling final exam practice questions. In the "My own solutions. docx" I have finished question 1,2,3,5 and some of question 6 and 7. And in " Other's solution. docx" there has another methods of question 1,3 and 5 that solved by my classmates. So please help me to compare and check both of my own solutions and other's solutions, to choose which method is the best one, if you find errors please help me to fix it. And also please help me to solved the whole question 4, and part (a), (b) of question 6 and 7 that I have not solved. Thanks. Please pay attention, after I accpted the solution, I will give the amount of $40 as tip.

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My own solutions.docx

Other's question 1 solution.docx

a) Here, To find out the LS estimator of β we minimize the above sum of square with respect to β.
Here this gives, b) From the data we have, Thus for the given data, and . c) We know that an estimate of σ2 is for a simple regression. But as here we don’t have an intercept term so the above formula becomes .
Now from the obtained results,
RSS = 0.709091
So, Thus,

Other's question 3 solution .docx

Here, To find out the LS estimator of β0 we minimize the above sum of square with respect to
β0. Here this gives,

Other's question 5 solution.docx

a) We know that,
Coefficient of determination = . The value 0.9815 tells us that this regression model is
explaining 98.15% of the total variation implying that the regression model fit the data
well. b) This test is done using a partial F test. Here the test statistic is,
F* =
So here, As this F test statistic follows a F(2,8) distribution thus p-value = P(F(2,8) > 0.64) =
0.5523
At 5% or 0.05 significance level we can see that the p-value of the test is larger than the
significance level thus we are failing to reject the null hypothesis.

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