Linear Regression Practice

As study time _______________, errors _______________.

• increases ; decrease
• increases ; increase
• decreases; decrease
• increases ; stays the same

Tags

CCSS.HSS.ID.A.1

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

Residuals are . . . 

• possible models not explored by the researcher
• variation in the response variable that is explained by the model
• the difference between the observed response and the values predicted by the model
• data collected from individuals that is not consistent with the rest of the group

Tags

CCSS.HSS.ID.A.4

Students in a science class investigated how the speed of changes with the air temperature outside. The data is shown in the scatterplot. Based on the scatterplot, what is the best prediction of the speed of sound when the air temperature is 50 degrees C?

• 350 m/s

• 355 m/s

• 360 m/s

• 380 m/s

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

Students in a science class investigated how the speed of changes with the air temperature outside. The data is shown in the scatterplot. If we use the scatterplot to predict the speed of sound when the air temperature is 50 degrees C, which is true?

• This is interpolation and an accurate prediction.

• This is interpolation and will lead to an inaccurate prediction.

• This is extrapolation and may not be an accurate prediction.

• This is extrapolation and will be an accurate prediction.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

The equation of the best-fit line is
y(hat) = 1.3 + 0.73x.  What is the residual for the point (4, 7)?

• 2.78
• 3.00
• 4.00
• 4.22

What is the best definition of the least squares regression line?

• The line that minimizes the squares of the horizontal distances between the data points and the line.
• The line that minimizes the squares of the vertical distances between the data points and the line.
• The line that minimizes the vertical distances between the data points and the line.
• The line that passes through the most number of data points.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

An influential point in the context of least square regression lines is a

• point far from all the other points
• point that, when omitted, causes the line to change significantly
• point that all other points are centered around
• None of these

Tags

CCSS.HSS.ID.A.3

CCSS.HSS.ID.B.6

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.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was  ŷ = 10 + 0.9x 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?

• 85.5

• 90

• 95

• 95.5

• none of these

Tags

CCSS.HSS.ID.C.7

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.

Tags

CCSS.HSS.ID.C.7