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WorksheetsLinear Models and Tables Review
Total questions: 15
Worksheet time: 8mins
The equation was ŷ = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
95
85.5
90
95.5
The equation was ŷ = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test, and on the final exam she scored a 98. What is the value of her residual?
3
2.5
-2.5
0
A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). Here is the residual plot from the least squares fit. What does the pattern of the residuals tell you about the linear model?
There is nothing to conclude.
The residual plot confirms the linearity of the fuel economy data.
The residual plot contradicts the linearity of the data.
In regression, the residuals are which of the following?
Factors unexplained by the data
The difference between the observed responses and the values predicted by the regression line
Data points which were recorded after the formal investigation was completed
Possible models unexplored by the investigator
Which of the following statements is TRUE about correlation coefficients (r)?
r values always have units
r values can be greater than 1
r values are used in the least squares regression line
r values describe the direction and strength for linear models
Suppose the following information was collected, where X = diameter of tree trunk in inches, and Y = tree height in feet.
If the LSRL equation is ŷ = -3.6 + 3.1x, what is your estimate of the average height of all trees having a trunk diameter of 7 inches?
18.1
19.1
20.1
21.1
Least-squares regression lines are resistant to outliers and influential points, and will not change.
True
False
Correlation coefficients are resistant to outliers and influential points, and will not change.
True
False
If dataset A of (x,y) data has correlation coefficient r = 0.65, and a second dataset B has correlation r = –0.65, then
The points in A exhibit a stronger linear association than B.
The points in B exhibit a stronger linear association than A.
Neither A nor B has a stronger linear association.
You can’t tell which dataset has a stronger linear association without seeing the data or seeing the scatterplots.
A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation is ŷ = 1,400 + 2,000x where y is the estimated raise and x is the performance rating. Which of the following statements are correct? Select ALL that apply
For each increase of one point in performance rating, the predicted raise will increase on average by $2,000.
This equation produces predicted raises with an average error (sum of residuals) of 0.
A rating of 0 will yield a predicted raise of $1,400.
The correlation for the data is positive.
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. Predict the number of chirps if the temperature is 68 degrees.
43 chirps
12 chirps
13 chirps
25 chirps
Suppose the correlation is negative. Given two points from the scatterplot, which of the following is possible? Select ALL that apply (make a sketch to help you!)
The first point has a larger x-value and a smaller y-value than the second point.
The first point has a larger x-value and a larger y-value than the second point.
The first point has a smaller x-value and a larger y-value than the second point.
Which of the following statements about residuals are true? Select ALL that apply
The mean of the residuals is always zero.
The regression line for a residual plot is a horizontal line.
A definite pattern in the residual plot is an indicator that a nonlinear model will show a better fit to the data than the straight regression line.
Residuals can only be positive.
Data are obtained for a group of college freshmen examining their SAT scores from their senior year of high school (x) and their GPAs during their first year of college (y). The resulting regression equation is ŷ = 1.35+ 0.4x. What does 1.35 represent in context?
A student's high school GPA of 0, predicts a GPS of 1.35 during their first year of college
A student's high school GPA of 1.35, predicts a GPS of 0 during their first year of college
A student's high school GPA of 0.4, predicts a GPS of 1.35 during their first year of college
A student's high school GPA of 1.35, predicts a GPS of 0.4 during their first year of college
Data are obtained for a group of college freshmen examining their SAT scores from their senior year of high school (x) and their GPAs during their first year of college (y). The resulting regression equation is ŷ = 1.35+ 0.4x. What does 0.61 represent in context?
For every increase in a student's high school GPA of 1, their first year of college GPA will increase by 0.4
For every increase in a student's high school GPA of 0.4, their first year of college GPA will increase by 1
For every increase in a student's high school GPA of 0.4, their first year of college GPA will increase by 1.35
For every increase in a student's high school GPA of 1.35, their first year of college GPA will increase by 0.4
