Statistics 2501 (001)
Assignment #2: Sept. 24, 2003
Due in class: Oct. 6, 2003

All problem numbers are from the textbook Statistics for Business and Economics, 8th Edition.

If a question does not specify if you should do it by hand or use Minitab, the choice is up to you.

1. If we measure the number of TV sets per person and the average life expectancy for the world's nations, there is a high positive correlation. In other words, nations with many TV sets have higher life expectancies.

   Could we lengthen the lives of people in Rwanda by shipping them TV sets? Explain why or why not. If your answer is no, give one possible explanation for the high correlation that is observed.

2. Suppose an inspired (but very bored) stats student was given a data set of 10 observations, and decided to put his/her calculator to work to calculate the following values from the data:
   
   $$SS_{xx} = 38.4, \quad \sum x_{i} = 42.9, \quad \sum y_{i}... ...quad \sum y_{i}^{2} = 4283.2, \quad \sum x_{i} y_{i} = -895.5$$
   
   
   You may also use the fact that SSE = 33.9. Now, complete the following:
   1. Find the least squares line.

   2. Calculate $R^{2}$ and $r$.

   3. Test whether there is a negative linear relationship between $x$ and $y$. Base your conclusion on the p-value of your test. Calculate your test statistic by hand. You can either use the T-table in the text to put a bound on the p-value, or you can use Minitab to find an exact p-value (Mark can show you how to do this, if you like).

   4. Find a 95% confidence interval for $y$ when $x_{p} = 3$. Do this by hand.

3. #10.37, pg. 485, using Minitab. Also, find a 99% prediction interval for a player's first anniversary ranking if they were ranked 21 on their wedding day. You can find this interval either by hand or using Minitab.

4. The president of a company that makes drywall wants to analyze the variables that affect demand for houses and offices (drywall is used to construct walls). The president decides to develop a multiple regression model in which the response variable is monthly sales of drywall (in hundreds of $4 \times 8$ sheets), and the explanatory variables are: the number of building permits issued in the county, 5-year mortgage rates, apartment vacancy rates and office building vacancy rates (all in percent). The data follow:

   Drywall	Permits	Mortgage	A Vacancy	O Vacancy
   328	49	8.35	2.98	13.43
   376	79	8.08	5.6	14.51
   373	79	7.9	2.25	14.24
   144	50	7.69	4.26	14.3
   194	37	7	2.6	11.64
   220	53	7.32	2.97	10.61
   126	22	8.4	5.35	18.45
   301	69	8.28	3.13	18.52
   54	21	8	5.6	10.29
   252	46	8.95	4.81	11.91
   381	79	8.21	5.88	17.75
   152	38	7.35	5.69	17.14
   351	73	7.27	4.86	16.11
   233	55	7.08	5.68	18.54
   35	12	7.76	4.46	19.46
   290	62	8.21	2.23	19.26
   5	12	7.76	5	17.28
   335	60	7.2	2.42	15.15
   280	49	7.57	3.25	19.94

   
   
   

   Complete the following, using Minitab whenever possible.

   1. Find the least squares equation that predicts the drywall sales from the explanatory variables.

   2. Interpret $\hat{\beta}_{2}$ in your equation in (a).

   3. Interpret $R^{2}$ in this problem.

   4. What would be the predicted monthly sales of drywall if 30 building permits were issued, mortgage rates were 8%, and vacancy rates for apartments and office buildings were 2.5% and 11%, respectively?

   5. Test at $\alpha = 0.01$ if your model appears to be useful in predicting drywall sales.

      NOTE: Make sure to save this data in Minitab, as we may use it in a future assignment.