Data analysis in business Tutorial 8

Question A

Use the simple regression model:

Y = β_{0 + β1X + ε,}

to answer the following True or False questions.

1. If b_{1 is a consistent estimator of β1, the sampling distribution of b1 will become more centered}

around β_{1 as the sample size increases.}

2. Let b_{0 denote the OLS estimate of β0. If the samples of X and Y are positive correlated, the}

sign of b_{0 will also be positive.}

3. If ε is not normally distributed, we can not use OLS to obtain unbiased estimates for β_{0 and β1.}

4. If R² of the regression is 0.2, it means 80% of the total variation in Y is explained by the

regression, and 20% of the total variation in Y is left unexplained.

Question B

An insurance company wishes to examine the relationship between the amount of life insurance held by a family and family income. From a random sample of 20 households, the company collected the data in the file T8_1.xlsx. The data are in thousands of dollars. Import the data into EViews and conduct the following exercise in EViews.

1. Draw a scatter diagram of the data to determine whether a linear regression model appears to

be appropriate.

2. Obtain degree of freedom corrected correlation and covariance between the two variables using EViews. Fill in the following table using the EViews output and round your results to three significant digits (see here for an explanation of significant digits).

The variance of insurance The variance of income The covariance between insurance and income The correlation between insurance and income

3. Write down a population linear regression model.

4. Compute the OLS estimate of β_{1 using the results from question B2 (round to 3 significant}

digits).

1

5. Estimate the linear regression model using the EViews. Write down the fitted model (round to

3 significant digits).

6. From the OLS estimates, how would the amount of life insurance change (on average) if income

increases by 3 thousands?

7. What is the R² of this regression?

Suppose that both the essential assumptions and the additional assumptions for OLS are satisfied and answer questions B8 and B9.

8. Write down the sampling distribution of b_{1 using the relevant statistics from EViews output.}

9. Conduct the following hypothesis testing at the 5% level (use step 3 to 5 of a hypothesis test, i.e., write down the null distribution of the test statistic, compute the value of the test statistic from sample, and draw a conclusion):

H_{0 : β1 = 1}

H_{A : β1 = 1.}

The post Data analysis in business Tutorial 8 appeared first on My Assignment Online.

Expert Help With This Assignment — On Your Terms