The following data represent a random sample of 5 observations. Assume that Y is a linear function of X and a normally distributed disturbance term with a mean of zero and a constant variance. In other words: Y = a + bX + u, u ~ Observati
The following data represent a random sample of 5 observations. Assume that Y is a linear function of X and a
|
Observation |
Y |
X |
|
1. |
1 |
17 |
|
2. |
3 |
13 |
|
3. |
5 |
8 |
|
4. |
7 |
10 |
|
5. |
9 |
2 |
Create a
Calculate the sample means, variances, and standard deviations of the variables X and Y either “by hand” or by using Excel and write one sentence describing what each of these mean in terms of the dataset.
The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand” using a calculator or in Excel in a manner that I can clearly see the formulas you have used. You should also check your calculations by entering the data into an Excel sheet and using the
- Calculate the standard errors for a and b (sa and sb). Discuss the interpretation of each of them.
- Compute the confidence interval (alpha = 0.05) and the t-statistic for b. Again, explain the meaning of each of them in a sentence.
3. Calculate the R2 for the regression and describe its meaning
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