AP Stats - 3.2 - Least Squares Regression

Which of the following is not a characteristic of the least squares regression line?

• The slope of the least squares regression line is always between 1 and -1

• The least squares regression line always goes through the point (x-bar, y-bar)

• The least squares regression line minimizes the sum of the squared residuals

• The slope of The least squares regression line will always have the same sign as the correlation

• The least squares regression line is not resistant to outliers

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CCSS.HSS.ID.A.3

CCSS.HSS.ID.C.8

Using data from the 2009 LPGA Tour, a regression analysis was performed using x = average driving distance and y = scoring average. Using the output from the regression analysis shown below, determine the equation of the least squares regression line.

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CCSS.8.EE.C.8C

Measurements (in centimeters) on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

By Looking at the equation of the least squares regression line, you can see that the correlation between height and arm span is

• greater than zero

• less than zero

• 0.93

• 6.4

• Can't tell without seeing the data

Tags

CCSS.HSF.LE.B.5

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

In addition to the regression line, the report on the Mumbai measurements says that  $r^2\ =\ 0.95$  . This suggests that

• although arm span and height are correlated, arm span does not predict height very accurately

• height increases by  $\sqrt{0.95}=0.97$  cm for each additional centimeter of arm span.

• 95% of the relationship between height and arm span is accounted for by the regression line

• 95% of the variation in height is accounted for by the regression line

• 95% of the height measurements are accounted for by the regression line.

Tags

CCSS.HSF.LE.B.5

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child's residual is

• -3.2 cm

• -2.2 cm

• -1.3 cm

• 3.2 cm

• 62.2 cm

Tags

CCSS.8.EE.C.8C

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

Suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. What effect will adding this child have on the correlation and the slope of the least squares regression line?

• Correlation will increase, slope will increase

• Correlation will increase, slope will stay the same

• Correlation will increase, slope will decrease

• Correlation will stay the same, slope will stay the same

• Correlation will stay the same, slope will increase.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

Suppose that the measurements of arm span and height were converted from cm to meters by dividing each measurement by 100. How will this conversion affect the values of r² and s?

• r² will increase, s will increase

• r² will increase, s will stay the same

• r² will increase, s will decrease

• r² will stay the same, s will stay the same

• r² will stay the same, s will decrease

Tags

CCSS.HSF.LE.B.5

A cell phone company charges $60.00 a month for up to 1 gigabyte computations. of data. The cost of additional data is $0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges at the end of the month, which linear equation can be used to determine a user’s monthly bill? 

• c = 60 - 0.05d
• c = 60d - 0.05
• c = 60.05d
• c = 60 + 0.05d

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

Some data were collected on the weight of a male white laboratory rat for the first 25 weeks after its birth. The linear regression equation is:
Weight = 100 + 40(Time).
Which is the best description of the slope for this regression equation in context of the problem?

• The slope of the line of regression is the time since birth of the rate. It demonstrates the predicted weight of a laboratory rate after so many months since birth.
• The slope is 40 grams/week which means the mouse gains about 40 grams per week after birth.
• The slope is 40 and it means for every increase in weeks the graph will increase. 
• The slope is 40, which tells us the line increases. 

Tags

CCSS.HSF.LE.B.5

How do you calculate a residual?

• Observed - Predicted
• Predicted - Observed