BA 282: Applied Business Statistics, Quiz 7: Regression Analysis and Chi-square
- In regression analysis, which of the following is described by the following definition? The amount of change in the value of the response variable (Y) for every unit change in the predictor variable (X)
- R
- R^{2}
- a (y-intercept)
- b (slope)
- fitted y
- Which of the following interval estimates is used when one wants to estimate the true value of a response variable (Y) for a given value of the predictor variable (X) using a linear regression equation?
- Confidence interval
- Prediction interval
- Which of the following interval estimates is used when one wants to estimate the true average value of a response variable (Y) for a given value of the predictor variable(X)?
- Confidence interval
- Prediction interval
- Which of the following measures the amount (in percent) of variability in the response variable as explained by a regression model?
- correlation coefficient (R)
- coefficient of determination (R^{2})
- standard error of the estimate (s_{y/x})
- multicollinearity
- none of the above
- Which of the following will be considered as a dummy variable in a multiple regression model to be used for predicting the assessed value of homes in a certain community?
- Location
- Type of roofing
- Type of heating (gas or electric)
- Number of bedrooms
- All but (d) levels
Use the plot below for questions 6 to 12
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. Which of the following would NOT be true for the regression resulting from the data in the plot above?
- R^{2} close to 100%
- R close to 1
- s_{y.x} close to 0
- All of the above would be true
- None of the above (a-c) would be true
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. If computed, the sign of the slope (b) in the equation would be:
- a. Either positive or negative
- b. Positive
- c. Negative
- None of the above
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. The solid line in the plot represents:
- The actual Y values
- The residual values
- The actual X values
- The estimated Y values
- None of the above
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. The equation for the line going through the points would take the form of:
- a. Y = a + bX
- b. Y = a – bX
- c. Y = x -1
- d. Y = a + bX^{2}
- e. None of these is correct
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. Around what percentage of the variation in quantity sold can be explained by the price per unit at which the product is sold?
- Close to zero
- Close to 100 percent
- Close to -100 percent
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. In this particular problem, the researcher is trying to predict:
- a. Units sold based on per unit price
- b. Per unit price based on quantity sold
- c. Both Units sold and unit price
- d. None of the above is correct
- Refer to the scatter plot above, which represents the relationship between unit price of a certain product and quantity sold at various price levels. The correlation coefficient (r) of the problem, if computed, could be:
- a. close to +1.0
- b. close to 0
- c. close to -1.0
- Exactly 1
- None of the above
Retention of students is one of the largest problems facing colleges and universities today. Loss of students impacts revenues not only from tuition but from state and federal funding programs. If a university can understand what factors impact student retention it can form strategic plans aimed at keeping students enrolled. Academic performance is often cited as one reason that students leave. Data were collected from 20 colleges in the Midwest on the freshman retention rate (% of freshmen who stay for a second year) and the 25^{th} percentile score on the American College Test (ACT) examination. The scatterplot and regression output are shown below.
- The correlation between the response variable and the predictor variable could be best described as:
- Perfectly positively linear
- Perfectly negatively linear
- Positively correlated
- Negatively correlated
- No correlation exists
- What is the response variable in this problem?
- The university
- Freshmen students
- 25^{th} Percentile ACT Score
- Freshmen retention rate
- 20 Midwest Colleges
- What is the predictor variable in this problem?
- The university
- Freshmen students
- 25^{th} Percentile ACT Score
- Freshmen retention rate
- 20 Midwest Colleges
- How much variability in the Freshmen retention rate can be explained by academic performance (as measured by the 25^{th} percentile score on the ACT)?
- 0.4783
- 0.0049
- 22.9%
- None of the above
- Is the regression model significant at 0.01 significance level?
- Yes
- No
- Using the regression equation, a Midwest college has 20 as the 25^{th} percentile ACT score. This college’s predicted Freshman retention rate is:
- 0.478
- 22.9%
- 0.7864
- Using the regression equation, a Midwest college has 20 as the 25^{th} percentile ACT score. With 95% confidence, it can be concluded that this college’s true Freshman retention rate will be between
- 0.6958 and 0.8770
- 0.7684 and 0.8044
- For every point increase in the 25^{th} percentile ACT score, the Freshman retention rate is expected to:
- increase by 0.014
- increase by 0.7864
- decrease by 0.014
- decrease by 0.7864
- None of the above
Below is a partial data for selected health care systems (n=18) showing each health care system’s operating margin (computed as total revenue minus total expenses divided by total revenue plus net operating profits) and percent of equity financing (fund balance divided by total assets). Use the scatter plot below to answer the following questions:
- The correlation between the response variable and the predictor variable could be best described as:
- Perfectly positively linear
- Perfectly negatively linear
- Positively correlated
- Negatively correlated
- No correlation exists
- What is the response variable in this problem?
- Percent of Equity Financing
- Percent Operating Margin
- What is the predictor variable in this problem?
- Percent of Equity Financing
- Percent Operating Margin
- Given the regression model, for every percentage point increase in a health care company’s equity financing, by how many percentage points does operating margin increase?
- -7.9356
- 2736
- 6759
- 8221
- None of the above
- How much variability in the response variable can be explained by the independent variable?
- -7.9356
- 0.2736
- 0.6759
- 0.8221
- None of the above
- Blue Shield Health Systems has 40 percent equity financing. What is the expected percent operating margin for BSSH?
- -7.9356
- 2736
- 6759
- 8221
- None of the above
Analysts at a company that produces small appliances are looking at sales of food preparation products in a medium-size city in the Midwest. They have noticed that sales in this city have not been meeting forecast values for several months and want to look at the problem in more detail. They have collected data on monthly sales ($), advertising expenditure ($), number of competing products available, number of discount opportunities (sales, coupons, etc.) offered during the month, and the warranty period of the item. The regression output is found below.
- What is the response variable in this problem?
- Sales
- Advertising
- Number of Competitors
- Discounts
- Warranty
- None of the above
- As advertising expenditures increase, what do you think the effect on sales will be?
- Sales will increase
- Sales will decrease
- No effect on sales
- As the number of competitors increase, what do you think the effect on sales will be?
- Sales will increase
- Sales will decrease
- No effect on sales
- What do you think the effect on sales will be by reducing Discounts?
- Sales will increase
- Sales will decrease
- No effect on sales
- Which of the following variables are qualitative?
- Sales
- Advertising
- Number of Competitors
- Discounts
- Warranty
- None of the above
- Based on the linear regression using all four independent variables, how much of the variation in the response variable is explained by the linear model?
- 0
- 7
- Not much
- 897
- 4%
- 457
- Which of the following variables have significant slopes (use alpha of 0.05)?
- Advertising
- Number of Competitors
- Discounts
- Warranty (in years)
- Number of Competitors and Warranty (years)
- Advertising and Discounts
- Which of the following variables is (are) not significant (use alpha of 0.05)?
- Advertising
- Number of Competitors
- Discounts
- Warranty (in years)
- Number of Competitors and Warranty (years)
- Advertising and Discounts
- What is the computed F for testing the significance of the model using the ANOVA F-test?
- 8
- 6
- 0000002
- 457
- 81
- Based on the signs of the slopes of the 4-variable linear regression model, does there appear to be multicollinearity in the model?
- Yes No
- Use the 4-variable linear equation. For each competitor that comes into the market, the company’s sales is expected to:
- Increase by $3,801
- Decrease by $3,801
- Increase by $510.2
- Decrease by $510.2
- Increase by $114
- Using the 4-variable linear equation, for each year the warranty is increased, the company’s sales is expected to:
- Increase by $3,801
- Decrease by $3,801
- Increase by $270.1
- Decrease by $270.1
- Using the 4-variable linear equation, the estimated sales for the following conditions: advertising expenditure of $400, zero competitor, 3 discounts, and 1 year of warranty – will be (use the closest value):
- $5,193
- $5,320
- $3,461
- Using a significance level of 0.01, is the 4-variable linear model significant?
- Yes No
Data from Consumer Reports New Car Buying Guide 2003-2004 of 43 vehicles (partial data shown below) was used to develop a multiple linear regression model to study fuel economy. City = EPA miles per in gallon city driving, Length = vehicle length (inches), Width = vehicle width (inches), Weight = weight (pounds), Japan = 1 if car maker is Japanese, 0 otherwise. The regression output is shown below the partial data.
- Which of the following is the response variable?
- City = EPA miles per in gallon city driving,
- Length = vehicle length (inches),
- Width = vehicle width (inches),
- Weight = weight (pounds),
- Japan = 1 if car maker is Japanese, 0 otherwise.
- Which of the following is a qualitative variable?
- City = EPA miles per in gallon city driving,
- Length = vehicle length (inches),
- Width = vehicle width (inches),
- Weight = weight (pounds),
- Japan = 1 if car maker is Japanese, 0 otherwise.
- Which of the following variables have significant slopes (use alpha of 0.05)?
- City = EPA miles per in gallon city driving,
- Length = vehicle length (inches),
- Width = vehicle width (inches),
- Weight = weight (pounds),
- Japan = 1 if car maker is Japanese, 0 otherwise.
- Which of the following variables is (are) not significant (use alpha of 0.05)?
- Length = vehicle length (inches),
- Width = vehicle width (inches),
- Weight = weight (pounds),
- Japan = 1 if car maker is Japanese, 0 otherwise.
- All of the above except Weight
- What is the computed F for testing the significance of the model using the ANOVA F-test? ____
- Is the model significant using significance level of 0.05?
- Yes
- No
- How strong is the correlation between the response variable and the predictor variables in the model?
- Not strong at all
- Somewhat strong ( at most 0.05)
- Moderately strong (0.5 to 0.7)
- Strong (0.70 to 0.90)
- Very strong (over 0.90)
A computer magazine surveyed its readers to determine how likely it was that people who planned to purchase new computers in the near future would buy a portable/notebook or desktop model. The results are tabulated here:
When Purchase Will be Made | |||
Type of Computer | 0 to 3 Months | 3 to 6 Months | 6 to 12 Months |
Notebook/Portable | 34 | 156 | 258 |
Desktop | 56 | 346 | 128 |
- Suppose you were interested in determining whether there is a relationship between the type of computer that a person is planning to buy and when the person plans to make the purchase, the appropriate statistical procedure in performing the analysis of the situation described above is:
- Chisquare Goodness-of-fit Test
- Chisquare Test of a Variance
- Testing Whether Two Nominal Variables are Independent
- None of the above
- If you were planning for stocking inventory for the period 0 to 3 months, which type of computer would you plan to carry more of in that planning period?
- Notebook/portable
- Desktop
- Neither of the above – will carry as many desktops as notebook computers
- What is the overall proportion of people who plan to purchase a Desktop computer within the next 12 months?
- 0.5133
- 0.3947
- 0.4581
- 0.5419
- None of the above
- Which of the following is the correct hypotheses setup?
- H0: Notebook and portable computers are independent
H1: Notebook and portable computers are dependent
- H0: Notebook and portable computers are dependent
H1: Notebook and portable computers are independent
- H0: Type of computer and When purchase will be made are independent
H1: Type of computer and When purchase will be made are dependent
- H0: Type of computer and When purchase will be made are dependent
H1: Type of computer and When purchase will be made are independent
- None of the above are correct
- Which of the following are the variables in the problem?
- Notebook/portable computers
- Type of Computer
- When purchase will be made
- 0 to 12 Months
- (b) and (c)
- None of the above is the correct answer
- Using the p-value as the decision rule, at significance level of 0.01, which of the following is the correct interpretation of the statistical conclusion?
- The variables notebook/portable and desktop computers are independent
- The variables notebook/portable and desktop computers are not independent
- The variables Type of computer and When purchase will be made are independent
- The variables Type of computer and When purchase will be made are not independent
- None of the above
A Web-based anonymous survey of students asked for a self-rating on proficiency in a language other than English and the student’s frequency of newspaper reading. Research question: At α = .10, is frequency of newspaper reading independent of foreign language proficiency?
Daily Newspaper Reading | ||||
Non-English Proficiency | Never | Occasionally | Regularly | Row Total |
None | 4 | 13 | 5 | 22 |
Slight | 11 | 45 | 9 | 65 |
Moderate | 6 | 33 | 7 | 46 |
Fluent | 5 | 19 | 1 | 25 |
Col Total | 26 | 110 | 22 | 158 |
- What are the variables in this problem?
- Frequency of newspaper reading
- Proficiency in a non-English language
- Frequency of newspaper reading and Proficiency in a non-English language
- Never, Occasionally, Regularly
- None, Slight, Moderate, Fluent
- If the decision rule is stated as: Reject H0 if Χ2 > Χ2 α,(r-1)(c-), what is the critical value for the test given a significance level of 0.10? ___________
- Perform the appropriate statistical analysis. Which of the following conclusions is correct?
- Reject H0 and conclude that the variables are dependent
- Fail to Reject H0 and conclude that the variables are dependent
- Reject H0 and conclude that the variables are independent
- Fail to Reject H0 and conclude that the variables are independent
- None of the above
A student rolled a supposedly fair die 60 times, resulting in the distribution of dots shown. Research question: At α = .10, can you reject the hypothesis that the die is fair?
Number of Dots | |||||||
1 | 2 | 3 | 4 | 5 | 6 | Total | |
Frequency | 7 | 14 | 9 | 13 | 7 | 10 | 60 |
- If the null hypothesis holds true, what is the expected number of 1’s to appear in the experiment?_______
- If the decision rule is stated as: Reject H_{0} if Χ^{2} > Χ^{2 }_{α,(k-1)}, what is the critical value for the test given a significance level of 0.10? ___________
- What is the p-value for the test? ___________
- Based on the output above, which conclusion is correct?
- Reject H0 and conclude that the die is not fair
- Fail to Reject H0 and conclude that the die is not fair
- Reject H0 and conclude that the die is fair
- Fail to Reject H0 and conclude that the die is fair
- None of the above
BA 282: Applied Business Statistics
Quiz 7
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2 | 22 | 42 |
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20 | 40 | 60 |