Question

The following ANOVA model is for a multiple regression model with two independent variables:

Degrees of            Sum of                 Mean

Source           Freedom            Squares                Squares       F      

Regression            2                    60

Error                   18                 120

Total                   20                 180

1. Determine the Regression Mean Square (MSR):

2. Determine the Mean Square Error (MSE):

3. Compute the overall F_stat test statistic.

4. Is the F_stat significant at the 0.05 level?

5. A linear regression was run on auto sales relative to consumer income. The Regression Sum of Squares (SSR) was 360 and the Sum of Squared Errors (SSE) was 120, what is the R-squared (r²) (Coefficient of Determination)?

6. 100 observations (n=100) were used to generate the regression in #5. Calculate the adjusted r-squared:

7. Another independent variable, the average automobile price increase was added to the model and the Regression Sum of Squares (SSR) went up to 400 and the Sum of Squared Errors (SSE) fell to 80. Calculate the new adjusted r-squared and answer whether you would use the new variable or not.

Using the same regression from the page before, a builder builds an 8,000 square foot house with a fireplace.

9. What does the regression model forecast the assessed value to be?

10. What is the plus and minus one standard deviation range around that estimated assessed value?

11. If a fireplace costs $3,000 to install, are you confident you will make a profit at the 90% level?

12. State whether the answer to the problem uses one tail or two tails of the distribution (2 points each)?

1. A prescription product is made in the form of a standard pill. The specified weight of the active ingredient is 10 grains per pill. Weights delivered by the production process are normally distributed with a standard deviation of 0.2 grains. The process is checked every quarter hour by weighing the active ingredient in each of a random sample of 16 pills. The sample mean is used with action limits. If a sample mean falls outside these limits, the process is stopped and checked. Otherwise it continues uninterrupted.

__________________________  

2. A shareholders group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of 7.27 with a standard deviation of 6.38 years. What is the probability that the mean tenure is 9 years?

_________________________    

3. In a factory, the current machine has an output of 32.1 units per minute. A new machine is available. If the machine can produce more than 38 units per minute, it will pay to change over to this new type. Three experienced operators have made experimental runs on four of the new machines. The mean of the sample of 12 runs is 39.4 units per minute and the standard deviation of the sample is 1.7 unites per minute. At the 0.005 (0.5%) significance level, does a hypothesis test justify purchasing the new machine?

_________________________    

13. Which distribution is closest to normal?                _________

1. 70% occur within one standard deviation, 93% occur within two standard deviations.
2. 78% occur within one standard deviation, 98% occur within two standard deviations.
3. 50% occur within one standard deviation, 72% occur within two standard deviations.

14. What does the Central Limit Theorem say about the characteristics of the sample means taken from random samples from a population? _____
    1. They are negatively skewed.
    2. They are normally distributed.
    3. They are positively skewed.
    4. They are uncorrelated.
    5. They are uniformly distributed.

15. For the following events, would you use the classical method (equally likely events), relative frequency, or subjective method as the basis for assigning probabilities (2 points each)?

1. The probability a total of six comes from a roll of two dice.

_______________

2. The probability of heads from the flip of a coin.

_______________   

3. The probability that a particular participant will win the World Series of Poker.

______________  

                 

Match the description with the definition. There are more definitions than name descriptions so some will be left blank. Do not apply a name description to more than one definition.               (2 points each)

16. Type I error                                    ______
17. Type II error                                   ______
18. Cross Sectional Data                        ______
19. Multicollinearity Problem                 ______
20. Null Hypothesis                               ______
21. Mutually Exclusive                          ______
22. Time Series Data                             ______
23. Permutation                                    ______

1. Collect the samples of preselected experts in the subject matter.
2. Error data where knowing the error at time t can explain the error at time t+1.
3. Data points are each associated with a particular period of time
4. Represents something you try to prove that is inconsistent with a hypothesis
5. Occurs if you reject the null hypothesis when it is true and should not be rejected.
6. When some betas calculated in a multiple regression are misleading because some of the variables have a correlation greater than 0.7 or less than -0.7.
7. The probability of occurrence of a particular outcome from a set where the order is important.
8. Outcomes where the probability of both occurring at the same time is zero.
1. Respondents feel obligated to please the interviewer.
10. Data that are collected for multiple subjects at approximately the same time.
11. The probability of occurrences of a particular outcome from a set.
50. Data that are collected from different types of subjects to match population characteristics.
1000. Represents the status quo or current belief about a situation.
14. Occurs if you do not reject the null hypothesis when it is false and should be rejected.

24. Which data sources are a population and which are a sample (1 point each)?

1. The average tuition cost paid by students in the University of California Higher Education System.

___________  

2. The average undergraduate tuition cost paid by parents of college students who reside in California based on a survey by the California department of higher education?

___________    

3. The average cost of rare earth held in Intel’s raw material inventory?

___________  

4. The number of people who voted for Jill Stein in Connecticut in the last presidential election?

___________  

5. The Nielson publication of how many watched the Super Bowl in February 2019?

___________   

25. Use the regression results on last page (each question 3 points):

1. The first regression just uses one variable. Do the results of the second regression merit using the second variable? Explain using the statistic that backs you up.

2. In the second regression, which variable is more significantly greater than zero? Quote statistics to back you up.

3. If independent variable 1 is 1% and independent variable 2 is -1%, what is your point estimate for the dependent variable and within what range are you likely to be 95% of the time?

4. For the beta for the second independent variable in the second regression, at the 95% confidence level, is the beta estimate different from 0.5?

5. The variable beta in regression 1 is similar to the sum of the betas in regression 2. What statistic should you look at to see if multicollinearity is a problem and given that statistic, is it?

25)

Attached is the regression output of assessed home values regressed against the square feet of the home (in thousands) and whether (1) or not (0) a home has a fireplace. d Value Analysis 4 Multiple R 0.9006 08111 0.7796 R Square 6 Adjusted R Square 7 Standard Error 8 Observations 10 ANOVA 12 Regression 13 Residual 14 Total 15 16 17 Intercept 18 Size 19 FireplaceCoded 263.7039 131.8520 25.7557 614321 5.1193 325.1360 0.0000 12 nts Standard Error tStat P-value Lower 95% 4.3517 45.9803 0.0000 2.5744 6.2871 0.0000 1.2412 3.1042 0.0091 95% 90.6090 209.5719 10.5766 21.7951 6.5574 200.0905 16.1858 3.8530 1.1486 8) Realtors' had been using a rule of thumb that 1000 square feet (%) added $20,000 to assessed value (%) Test the null hypothesis that Ho: β1-20 at the 10% level (2 sided test.) SUMMARY OUTPUT ssion Stanstis Muiple R R Square Adjusted R Squere Slandard Emer Osse vatiers 0755850224 0.571309562 0.570037483 0027264784 ANOVA MS 10.333857940.33385794449.115T5 5.9517E-54 37 0250615161 0.0007 3368 338 0.584373101 Total Coemcies Standerd Era 0.000349189 0.001539622 -0.22699674 0.820563913 0.003377959 0.C0257899-0.0033779690.00267899 р.vau9 Lower 95% r 9556 Lower 95.0% 95.0 Imercept x Var 33e 1.253071356 0.059 12852 19233445.9517E-64 136763895 1.369378838 1.135763895 1369378838 SUMMARY OUTPUT 2 9ssion Stanstics Muliple R R Square Adjusted R Squere Slandard Emer Opse vatiers 0.885277843 0.783716859 0.78242946 019394857 MS 2 04579305 0.228991526 608.7595735 1.9222E-112 3 0.15 0.000375161 Total 0.58437310 Coemcies Standerd Era 0000275195 0.001095221 0.251258578 0801760066 0.002429549 0.C01879159-0.002 29619 0001879159 0.652702947 0.05349256 12.20172907 1.34928E-28 0.547481243 0.757925651 0.547 80243 0.757925551 p-uglus Lower 95% r9556 Lower 95.0% しkper 95.056 Imercept x Varase 1 Coumn1 Column 0.51781654

Answer 1

1. Regression mean square

2 60 30

2. Error mean square

120 20 18 = 3

3. Overall Fstat test statistic

tegression Mean square 309 -W =- 20 ETTOT mean square

4. Checking if Fstat is significant at 0.05 level

F2,18,1-0.05- 3.56

Since Fstat test statistic is greater than 3,56, it is significant.

5. Coefficient of Determination

Regression Sum of Squares (SSR) = 360

Sum of Squared Errors (SSE) = 120

Coefficient of Determination is given by:

SSR 360 3603 SSR+SSE 360 120 480 4