Assignment Four: Quiz on Friday Feb. 15th

Using the FURNACE data again, carry out analyses (elementary significance tests) to answer these questions. There is not necessarily a separate SAS procedure for each question. In each of your analyses, there is one independent variable and one dependent variable, and you should be able to state what they are. You can get the statistics you need by running proc freq, proc corr, proc reg, proc means and proc glm --- not necessarily in that order, and you may not need all of them.

For the chisquare test of independence, please pay attention to the first one SAS gives, which is the familiar Pearson chisquare. If you use proc glm to test differences among more than 2 means, follow up any significant differences with Scheffé tests. That way you will be able to say which means are significantly different from each other.

1. If you observe the shape of a house's chimney, does that improve your ability to predict what type of furnace the house has?
   1. What is the value of the test statistic? The answer is a number.
   2. What is the p-value? The answer is a number.
   3. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   4. If the results are significant, state the conclusion in plain, non-statistical language. If they are not significant, write "No conclusion.".
2. Is there more average energy consumption with the vent damper active (in), or inactive (out)?
   1. What is the value of the test statistic? The answer is a number.
   2. What is the p-value? The answer is a number.
   3. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   4. If the results are significant, state the conclusion in plain, non-statistical language. If they are not significant, write "No conclusion.".
3. Is there a tendency for houses that consume lots of energy with the vent damper inactive to also consume a lot of energy with the vent damper active?
   1. What is the value of the test statistic? The answer is a number.
   2. What is the p-value? The answer is a number.
   3. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   4. If the results are significant, state the conclusion in plain, non-statistical language. If they are not significant, write "No conclusion.".
   5. What proportion of the variation in energy consumption with vent damper active is explained by energy consumption with vent damper inactive? The answer is a number. If you need a calculator to answer this question, bring the calculator to the quiz.
4. Does energy consumption depend on type of vent damper? Your dependent variable should be the difference of two variables in the raw data file. This way energy consumption with vent damper inactive serves as a baseline for energy consumption with vent damper active.
   1. What is the value of the test statistic? The answer is a number.
   2. What is the p-value? The answer is a number.
   3. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   4. If the results are significant, state the conclusion in plain, non-statistical language. If they are not significant, write "No conclusion.".
   5. What proportion of the variation in the dependent variable is explained by type of vent damper? The answer is a number. If you use proc glm, the number is on your printout.
5. Does average amount of energy consumption with vent damper inactive depend on type of chimney liner?
   1. What is the value of the test statistic? The answer is a number.
   2. What proportion of the variation in the dependent variable is explained by type of chimney liner? The answer is a number.
   3. What is the p-value? The answer is a number.
   4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   5. If the results are significant, which means are different from each other? Describe the results in plain, non-statistical language. If the results are not significant, write "No conclusion.".
6. Do different kinds of house tend to have different types of chimney? Please use the expected option as well as chisq on proc freq, so you can see the expected frequencies.
   1. What is the value of the test statistic? The answer is a number.
   2. What is the p-value? The answer is a number.
   3. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   4. What is the smallest expected frequency? Because of this, we'd better not interpret the results. Make a new variable that classifies houses as either Ranch, Two-story or Other, and re-do the question. SAS still complains about low expected frequencies, but the lowest one is greater than one, so we won't worry about it. What percentage of Ranch houses have round chimneys? What percentage of Two-Story houses have round chimneys? What percentage of Other houses have round chimneys?
7. Make a new variable that is house age at or below the median versus house age above the median (You'll need to do proc means or proc univariate in a separate run to find out the median). Using this new binary variable, do older houses tend to use more energy with the vent damper inactive?
   1. What is the value of the test statistic? The answer is a number.
   2. What proportion of the variation in the dependent variable is explained by the independent variable? The answer is a number.
   3. What is the p-value? The answer is a number.
   4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   5. If the results are significant, describe the results in plain, non-statistical language. If the results are not significant, write "No conclusion.".
   6. Why did we split house age at the median instead of doing a simple regression?
8. Is there any connection between chimney height and chimney type?
   1. What is the value of the test statistic? The answer is a number.
   2. What proportion of the variation in the chimney height is explained by chimney type? The answer is a number.
   3. What is the p-value? The answer is a number.
   4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   5. If the results are significant, which means are different from each other? Describe the results in plain, non-statistical language. If the results are not significant, write "No conclusion.".
9. Is energy consumption with vent damper active related to type of damper?
   1. What is the value of the test statistic? The answer is a number.
   2. What proportion of the variation in energy consumption with vent damper active is explained by type of damper? The answer is a number.
   3. What is the p-value? The answer is a number.
   4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
   5. Did you do follow-up tests? Why or why not?
   6. If the results are significant, describe the results in plain, non-statistical language. If the results are not significant, write "No conclusion.".
10. What proportion of the variation in energy consumption with vent damper active is explained by chimney height? Is it significant?
11. Carry out an analysis in which the dependent variable is the difference in energy consumption between damper active and damper inactive, and the independent variable is type of furnace.
    1. What is the value of the test statistic? The answer is a number.
    2. What proportion of the variation in the dependent variable is explained by the independent variable? The answer is a number.
    3. What is the p-value? The answer is a number.
    4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
    5. If the results are significant, which means are different from each other? Describe the results in plain, non-statistical language. If the results are not significant, write "No conclusion.".

Bring both your log file and your list file to the quiz. Do not write anything on the printouts except your name and student number. You may be asked to hand one or both of them in. These two files must be generated by the same program or you will lose a lot of marks. If there are harmless errors or warnings in your log file, be prepared to explain them.