Part 1. 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 ~ (0,2)

Observation Number Y X 1 2 11 2 4 14 3 6 10 4 8 8 5 10 6 6 12 5 7 14 4 8 16 3 9 17 2 10 18 1

1. Create a scatterplot of this dataset (either manually, or by using Excel graphing functions) 2. 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 regression analysis function under Data Tools. 3. Show how to calculate a and b. In a sentence, discuss the interpretation of each of them. 4. Calculate the predicted value of Y and the residual for each observation. 5. Calculate the Sum of Square Errors (SSE), Mean Square Error (MSE) and the Standard Error (s). Explain the meaning of each of them.

6. Calculate the standard errors for a and b (sa and sb). Discuss the interpretation of each of them. 7. Compute the confidence interval (alpha = 0.05) and the t-statistic for b. Again, explain the meaning of each of them in a sentence. 8. Calculate the R2 for the regression and describe its meaning. 9. Graph the data points and the sample regression function. Identify the slope and the intercept term. Label the data points and graphically indicate the residual for each observation. Add a vertical dashed line for the mean of X and the horizontal dashed line for the mean of Y. Does the regression function pass through the intersection of these two lines?