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WorksheetsAP Stats - Unit 4 - Exploring 2-Variable Data
Total questions: 25
Worksheet time: 4hrs 10mins
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and y (as described by the regression equation).
A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.
y = 1.5x + 12
y = 12x + 1.5
y = 0.67x - 8
y = -8x + 0.67
With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student’s completion time on a new puzzle was measured. The Residual plot for regression of Completion Time on Practice Time is shown below. Which of the following is correct?
There is a no relationship between Practice Time and Puzzle Completion Time.
This regression equation would likely overestimate the Puzzle Completion Time for 175 minutes of practice time.
There is a non-linear relationship between Practice Time and Puzzle Completion Time.
There is a linear relationship between Practice Time and Puzzle Completion Time.
Other things being equal, larger automobile engines are less fuel efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in mpg) of sport utility vehicles. In this study
gas mileage is a response variable, and you expect to find a negative association.
gas mileage is a response variable, and you expect to find a positive association.
gas mileage is an explanatory variable, and you expect to find a strong negative association.
gas mileage is an explanatory variable, and you expect to find a strong positive association.
gas mileage is an explanatory variable, and you expect to find very little association.
Which statements below about least-squares regression are correct?
I. Switching the explanatory and response variables will not change the least-squares regression line.
II. The slope of the line is very sensitive to outliers in the x direction with large residuals.
III. A value of r^2 close to 1 does not guarantee that the relationship between the variables is linear.
Only I
Only II
Only III
Both II and III
I, II, and III
A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is ŷ = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating.
Which of the following statements must be true?
For each one-point increase in performance rating, the raise will increase on average by$1400.
The actual relationship between salary raises and performance rating is linear.
The residuals for half the observations in the dataset will be positive.
The correlation between salary raise and performance rating is negative.
If the mean performance rating is 1.2, then the mean raise is $3800.
For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by ŷ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months).
Loretta is 20 months old and is 80 cm tall . What is her residual?
-2.47
2.47
-12.6
12.6
77.53
You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. “Least-squares” refers to
Minimizing the sum of the squares of the 25 houses’ heating costs.
Minimizing the sum of the squares of the number of rooms in each of the 25 houses.
Minimizing the sum of the products of each house’s actual heating costs and the predicted heating cost based on the regression equation.
Minimizing the sum of the squares of the difference between each house’s heating costs and number of rooms.
Minimizing the sum of the squares of the residuals.
