QMETH 201 - University of Washington



QMETH 520 Review Questions

Question 1:

A. Describe the scatterplot on the right

A linear relationship with an outlier

A linear relationship with unequal variability

A skewed distribution

A nonlinear relationship

B. The scatterplot of the sales against the advertisement expenditure for 10 supermarkets is shown below. Do you think that the linear regression will work? Yes No Circle one.

If you circle No, please state your reason in one sentence. Use the space to the right of the scatterplot.

C. Emily uses the method of least squares to develop a predicting equation for the 1998 return. From the following five statements, please select one that best explains the method. If you cannot find an appropriate one, please explain.

1. The method minimizes the prediction residuals for all observations.

2. The method minimizes the sum of residuals for all observations.

3. The method minimizes the sum of absolute residuals for all observations.

4. The method minimizes the sum of squared residuals for all observations.

5. The method minimizes the number of observations that do not lie on the prediction line.

D. A marketing manager wants to develop a 95% prediction interval of the company sales. Beside the regression line, the manager needs to compute:

1. all residuals of the regression.

2. the R-squared value of the regression.

3. the standard error of the slope.

4. the standard error of estimate.

E. T or F.

“The sample correlation coefficient, r is used to measure how strong the relationship is regardless of the shape of scatterplot. This is why r is useful.”

F. The sample correlation coefficient is zero. This means:

1. the regression line has the intercept of 0.

2. the regression line has a slope of 1.

3. the regression line is parallel to the X-axis.

4. the regression line cannot be computed.

G. The standard error of the slope is used:

1. to test if the regression is illusory.

2. to construct a prediction interval.

3. to indicate the average increase of Y given one unit increase of X.

4. to indicate how much variability of Y can be explained by X.

H. T or F.

“The sample regression equation plus or minus one standard deviation of the dependent variable Y should contain about 68% of scatter points, when the histogram of Y is normal.”

I. The correlation coefficient between the price change of an IBM stock during one week and that of the following week is 0. Therefore the regression slope for forecasting the next week’s price change by this week’s price change must be 0.

True False Circle one.

If you circle false, please state your reason in one sentence.

J. A research hypothesis on a sample regression coefficient is accepted at the significance level of 5%. This inference is subject to Type II error. Fortunately the probability is only 5%.

True False Circle one.

If you circle false, please state your reason in one sentence.

Question 2

Tom Clancy develops an equation that will predict manpower needs for US Naval hospitals. He collects data for seventeen sites around the world. The dependent variable is the monthly labor-hours. The explanatory variables are workload variables, i.e., factors that affect the manpower in a hospital installation. See below:

Y = monthly labor-hours,

X1 = average daily patient load,

X2 = monthly X-ray exposures,

X3 = monthly occupied bed days,

X4 = eligible population in the area in 1000, and

X5 = average length of patients' stay in days.

For each of these six variables, the average, the standard deviation, and the correlation coefficient with the dependent variable are computed and shown in the table below.

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a. Of the five independent variables X1 through X5, which variable appears to produce the best regression prediction of Y? Please explain.

b. Compute the regression equation for predicting Y using the best variable that you selected in a, including the standard error of estimate (approximate). Please show your work.

Question 3

Phil Perry, the Managing Partner of Dante Investors, Inc., determines how strongly the sales generated by a broker of Dante are related to the number of new clients a broker signs up with the firm. He uses linear regression. He collects a random sample of 12 brokers and assembles the data in the table below. See Table 1. He then uses the Excel Regression routine to compute the regression. See Table 2.

Table 1: Data Used for Regression

|Broker |Number of Clients |Sales Generated ($1000) |

|1 |27 |52 |

|2 |11 |37 |

|3 |42 |64 |

|4 |33 |55 |

|5 |15 |29 |

|6 |15 |34 |

|7 |25 |58 |

|8 |36 |59 |

|9 |28 |44 |

|10 |30 |48 |

|11 |17 |31 |

|12 |22 |38 |

Table 2: Excel Regression Output

|SUMMARY OUTPUT | | | | | | |

|Regression Statistics | | | | | |

|Multiple R |0.886 | | | | | |

|R Square |0.785 | | | | | |

|Adjusted R Square |0.763 | | | | | |

|Standard Error |5.804 | | | | | |

|Observations |12 | | | | | |

| | | | | | | |

|ANOVA | | | | | | |

| |df |SS |MS |F |Significance F | |

|Regression |1 |1227.38 |1227.38 |36.43 |0.000125906 | |

|Residual |10 |336.87 |33.69 | | | |

|Total |11 |1564.25 | | | | |

| | | | | | | |

| |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% |

|Intercept |17.692 |4.941 |3.581 |0.005007151 |6.682 |28.701 |

|X Variable 1 |1.119 |0.185 |6.036 |0.000125906 |0.706 |1.532 |

a. Identify the independent variable and the dependent variable used in the regression.

b. Write the forecasting equation suggested by the Excel output

c. Find the predicted sales and the residual for the first data pair.

d. What are the estimated sales attributable to a single additional new client that a broker signs up?

e. What is the sales revenue of a broker who recruits 40 new clients? Construct a 95% interval prediction.

f. What is the 95% confidence interval for the expected marginal value of an additional new client that a broker signs up?

g. What are the appropriate Null hypothesis and the Research (alternative) hypothesis being tested in this regression model? Use β to stand for the population regression slope.

h. Using the confidence interval method can you reject the Null hypothesis at the 5% level of significance? Please explain.

i. Using the t statistic method, this time at the 1% level of significance, can you reject the Null hypothesis? Please explain.

j. What percent of the sample variability of the sales revenue can be explained by the number of new clients recruited by each broker?

Question 4:

Samantha is excited that she is accepted by the Central University. The reputation of the institution is surging because of its innovative global management program. Samantha would like to buy a used car, because the university is located in a rural area. Samantha likes the Red Angel, an import. The Campus Times ads section lists the following used Red Angels for sale. See Table 1. Samantha uses Excel on the campus-computing server to run a regression. Due to Y2K bugs, some outputs are missing. See Table 2.

Table 1: Data (Sx=2.07, Sy =2.31)

Table 2: Regression Outputs

|Regression Statistics | | | | | |

|Multiple R |- 0.947 | | | | | |

|R Square |0.897 | | | | | |

|Adjusted R Square |0.880 | | | | | |

|Standard Error |(a) | | | | | |

|Observations |8 | | | | | |

| | | | | | | |

|ANOVA | | | | | | |

| |df |SS |MS |F |Significance F |

|Regression |1 |33.496 |33.496 |52.356 |0.000354 | |

|Residual |6 |3.839 |0.640 | | | |

|Total |7 |37.335 | | | | |

| | | | | | | |

| |Coefficients |Standard Error |t Stat |P-value |Lower 95% |Upper 95% |

|Intercept |(b) |0.584 |15.405 |0.0000 |7.569 |10.428 |

|X Variable 1 |(c) |(d) |(e) |0.0003 |(f) |-0.699 |

Please compute the values for (a) through (f). For each, please show your work.

a.

b.

c.

d.

e.

f.

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