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- 1. Multiple Choice
A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give x-bar= 8.4, sx = 2.1, y-bar= 14.2, sy = 3.8, and r = 0.86. What is the equation of the Least-squares line?
y-hat = -1.004 + 1.81x
y-hat = 1.096 + 1.56x
y-hat = 1.25 + 0.47x
y-hat = 5.8 + 0.86x
The equation cannot be determined from the given information
- 2. Multiple Choice
A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.
Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
Machine A always produced the same number of defective parts as machine B.
Machine A always produced fewer defective parts than machine B.
Machine A always produced more defective parts than machine B.
Machine A usually, but not always, produced fewer defective parts than machine B.
Machine A usually, but not always, produced more defective parts than machine B.
- 3. Multiple Choice
A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?
The relationship is linear because the correlation is positive.
The relationship is not linear because the correlation is positive.
The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.
The parties with a larger number of customers are associated with the shorter times elapsed until the party left the restaurant.
There is no relationship between the number of customers in a party at a table in the restaurant and the time required until the party left the restaurant.
- 4. Multiple Choice
A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output.
Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?
30
5
4
2.5
1/30
- 5. Multiple Choice
A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?
0.59 months per pound
0.59 pounds per month
0.59
0.59 months times pounds
0.59 month pounds
- 6. Multiple Choice
For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?
Yes, because 3 inches falls above the maximum value of lengths in the sample.
Yes, because the regression equation is based on a random sample.
Yes, because the association between length and weight is positive.
No, because 3 inches falls above the maximum value of lengths in the sample.
No, because there may not be any 3-inch fish of this species in the pond.
- 7. Multiple Choice
Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 years after partial-cut harvesting, and the percent of trees that were harvested in each of 11 forests.
Which is a plausible value for the correlation?
0.3
-1.0
-0.45
-0.78
0.82
- 8. Multiple Choice
A set of bivariate data was used to create a least-squares regression line. Which of the following is minimized by the line?
The sum of the residuals
The sum of the squared residuals
The sum of the absolute values of the residuals
The influence of outliers
The slope
- 9. Multiple Choice
The following is a residual plot for a linear regression of y
versus x.
What is indicated by the plot?
A linear model is appropriate.
A linear model is not appropriate.
Variability in y is constant for all values x.
At least one point is influential with respect to the regression.
At least one point is an outlier with respect to the regression.
- 10. Multiple Choice
A stats teacher collected data from her students most recent quiz and test scores. She found the relationship was fairly linear and that 87% of the variation in her student's test scores could be explained by their quiz scores.
What was the value of the correlation coefficient?
0.87
9.32
0.93
0.76
Not enough information
- 11. Multiple Choice
The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river.
Which of the following statements is a correct interpretation of the value 19.0 in the output?
On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.
On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.
The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.
The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.
Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.
- 12. Multiple Choice
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model
ŷ = 25.2 + 3.3x 9 < x < 25,
where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
3.3 ° F
16.5 ° F
25.2 ° F
28.5 ° F
41.7 ° F
- 13. Multiple Choice
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model
ŷ = 25.2 + 3.3x 9 < x < 25,
where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit.
If a biologist counted 13 chirps and measured an air temperature of 73 degrees, what is the residual?
68.1 ° F
- 3.2 ° F
- 4.9 ° F
3.2 ° F
4.9 ° F
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