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22S:008 Exam 2, Part I, Mar. 31, 2000 Name:_______________________________
Form B ID: _______________________________________
Please circle one. Discussion Section: 9:30, 10:30, 11:30, or 12:
Please enter all of your answers on these exam pages. There are 30 questions on this part. A Defective Question Report, Formula sheet, and Tables will be handed out separtely..
- The least squares regression line is that line which makes the sum of the vertical distances between the observation pairs and the fitted line as small as possible. A) True B) False
- What is the area under the standard normal curve between the z -scores of −0.91 and +1.3?
A) 0. B) 0. C) 0. D) 0. E) None of the above.
- A class has asked their instructor to “grade on the curve.” With this system the instructor is required to give preselected percentages of the various possible grades. In particular, the top 10% of the class must receive A’s. If exam scores are normally distributed with mean 82.0 and standard deviation 2.34, what exam score corresponds to the lowest A grade? A) 70 B) 75 C) 80 D) 85 E) 90
- Suppose y is a response variable of starting annual salary, x is a continuous predictor variable of years of education ( x = 12 means high school graduate, x = 16 means college graduate, etc.), and z is an indicator variable indicating gender ( z = 1 means female). Consider the regression model with equation: . What combination of coefficients represents the predicted starting annual salary for a female college graduate? A) b 0 + b 1 + b 2 B) 16 b 1 + b 2 C) 16 b 1 D) b 0 + 16 b 1 E) b 0 + 16 b 1 + b 2
- In general, the smaller the value of the adjusted R^2 , the better the regression model.
A) True B) False
y ˆ^ = b 0 + b 1 x + b 2 z
- A salary distribution is strongly skewed toward the high values. The mean of the distribution is $28,000 and the standard deviation is $10,000. What percentage of the salaries are below $38,000? A) 68% B) 82% C) 95% D) Essentially 100% E) Cannot be determined since the distribution of salaries is skewed.
- A salary distribution is strongly skewed toward the high values. The mean of the distribution is $28,000 and the standard deviation is $10,000. A sample of 49 of the salaries is selected randomly and the average of these salaries calculated. If this random sampling were repeated many times, what percentage of the sample averages would be below $38,000? A) 68% B) 82% C) 95% D) Essentially 100% E) Cannot be determined since the distribution of salaries is skewed.
- We discussed a “managed” dice-roll process where we adjusted the current dice total based on the last dice total in an attempt to roll more sevens. This example illustrates: A) improving an out-of-control process. B) how to find common causes of variation. C) how to reduce the variation in an out-of-control process. D) how to increase variation in an in-control process. E) how to find special causes of variation.
- Replication is important in experimentation since process results vary even under carefuly controlled experimental conditions. A) True B) False
- A portion of an ANOVA (analysis-of-variance) table from a multiple regression calculation is shown to the right. What is the value of s (the residual standard deviation) for this regression? A) 0. B) 0. C) 0. D) 0. E) 0.
Source SS df
Regression 0.427 3
Residual Error
Total 0.949 93
- A student collects some observational data on her fellow students. For 100 students, she obtains values on two variables: College GPA and Average Weekly Hours Watching Television. She finds the correlation coefficient between the two variables to be +0.95. We can therefore conclude that, for her 100 students, the scatterplot of College GPA versus Average Weekly Hours Watching Television would show a strong upward trend. A) True B) False
- There is a strong positive correlation between the number of highly specialized doctors at University Hospital and the proportion of patients that die at the hosptal. This is an example of: A) a lurking variable B) ecological correlation C) cause and effect D) consistency E) mechanism
- The graphic displayed below appeared in a recent Time Magazine dated April 3, 2000.
The far right says “THERE SHE GOES At this rate the BMI of Miss America could reach zero in about 320 years.” This is an example of:
A) extrapolation B) ecological correlation C) cause-and-effect D) a lurking variable E) None of the above.
- In the multiple regression example given in the British Steel video, they used two continuous predictor variables (amount of carbon in the steel plate and amount of carbon in the welding wires) to predict the amount of carbon in the final weld. Their regression model is best described as A) one line B) two parallel lines C) one quadratic curve D) a plane E) None of the above.
- We used an example of measuring the variation in Attentiveness in Lecture. In that example “Aaron’s daydreaming about Ames, Iowa” would be considered a common cause of variation. A) True B) False
- The results produced by a constant-cause system vary, and may vary over a wide band or a narrow band.
A) True B) False
- The three density histograms at the right display the results of finding average (mean) spots on 2, 5, or 10 dice tossed 6000 times. They are labelled A, B, and C. Which of the following is the correct order from 2 to 5 to 10 dice? A) A, B, C B) C, B, A C) B, A, C D) A, C, B E) B, C, A
- The graph at the right shows a plot of residuals versus x from a fitted straight-line model. Which of the following best describes what we learn from this graph? A) Since the graph is mound-shaped the plot indicates that the straight-line model explains the relationship well. B) Since the residuals sum to zero the plot indicates that the straight-line model is a good fit for the relationship. C) Since about half of the residuals are positive and half negative the plot indicates that the straight-line model is a good fit for the relationship. D) Since the graph shows zero correlation between residuals and x the plot indicates that the straight-line model could be improved. E) Since the graph shows a systematic pattern in the residuals—negative then positive then negative—the plot indicates that the straight-line model could be improved—possibly with a quadratic model.
- A basketball coach has an idea that training in ballet might help her players jump higher. To test this idea she divides her team randomly into two equal groups. One group is required to take six weeks of ballet training before the basketball season begins. The other group receives no ballet training. This study would be classified as A) a probability survey B) an observational study C) an experiment D) an observational survey E) None of the above.
1 2 3 4 5 6
Mean
Density
1 2 3 4 5 6
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Density
1 2 3 4 5 6
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A
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0 5 10
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- The times necessary to complete service for a class of bank customers is described by a normal distribution with mean 10 minutes and standard deviation 2 minutes. Service times are considered excessive if they exceed 15 minutes. Over the long run, what percent of customers will experience excessive service times? (Show your work.)
Answer = ____________
- An analysis of 27 pairs of data produced a least squares regression line with equation. (Show all of your work.)
a) The fitted value when x = 3 is ________________
b) The residual when x = 3 and y = 31 is ______________________
y ˆ^ = 23 + 3 x
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- Open the Worksheet named cars.mtw from the 22s:008 datasets. These data give values on several variables for 45 cars. We will just look at TripMPG (in miles per gallon for driving on a Trip), Weight (in pounds), and Trans (transmission type with 1=automatic, 0=manual). a) Use the Weight variable alone to “explain” the response variable, TripMPG.
The least squares regression line has equation: _____________________________________
The residual standard deviation for this model is ______________ with __________ degrees of freedom.
The coefficient of determination for this model is: R^2 = _________ % and the adjusted R^2 is _________ %.
b) Now fit a model that uses both Weight and Transmission Type (Trans) to explain TripMPG.
The least squares regression equation is: _______________________________________________
The residual standard deviation for this model is ______________ with __________ degrees of freedom.
The coefficient of determination for this model is: R^2 = _________ % and the adjusted R^2 is _________ %.
How much does the Automatic Transmission “cost us” (in MPG) versus a Manual Transmission for a car of the same Weight? _________________
