AP Stats Unit 2 Quiz

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 + .63𝑥, where y represents height (in centimeters) and x represents age (in months). If Joseph is 22.5 months old, what is his predicted height?

• 50.80 cm

• 64.96 cm
  
  

• 65.96 cm

• 79.11 cm

• 87.40 cm

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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 + .63𝑥, where y represents height (in centimeters) and x represents age (in months). Loretta is 20 months old and 80 cm tall.  What is her residual?

• -2.47 cm

• 2.47 cm
  
  

• -12.60 cm

• 12.60 cm

• 77.53 cm

You have data for many families on the parents’ income and the years of education their eldest

child completes. Your initial examination of the data indicates that children from wealthier families

tend to go to school for longer. When you make a scatterplot,

• the explanatory variable is parents’ income, and you expect to see a negative association.

• the explanatory variable is parents’ income, and you expect to see a positive association.

• the explanatory variable is parents’ income, and you expect to see no association.

• the explanatory variable is years of education, and you expect to see a negative association.

• the explanatory variable is years of education, and you expect to see a positive association.

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The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

• much smaller than 0.52

• slightly smaller than 0.52

• unchanged: equal to 0.52

• slightly larger than 0.52

• much larger than 0.52

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An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that

• when corn prices are above average, soybean prices also tend to be above average.

• there is almost no relation between corn prices and soybean prices.

• when corn prices are above average, soybean prices tend to be below average.

• there is not enough information to determine the relationship between the soybean prices and corn prices.

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Which of the following are true statements?

I. Correlation requires that there are clearly-identified explanatory and response variables.
II. Scatterplots require that both variables be quantitative.
III. Every least-squares regression line passes through

 $\left(\overline{x},\ \overline{y}\right)$  

• I and II

• I and III

• I, II, and III

• III

• II and III

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There is an approximate linear relationship between the cost of a plane ticket (y dollars) and number of days until the flight (x days) described by the equation ŷ = 500.3 - 6.1x, Which one of the following statements must be true?

• The cost of the ticket will decrease $6.10 for each day earlier the ticket is booked in advance.

• The correlation between ticket price and number of days prior to the flight is strong and positive.

• We can conclude that the typical cost of a ticket is $500.30

• The cost of the ticket typically varies by $6.10 from the mean price of $500.30.

• A person who paid $450 for a ticket 3 days prior to the flight paid more than expected.

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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 squares of each house’s actual number or rooms and the predicted number of rooms 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 house’s actual heating costs and the predicted heating cost based on the regression equation.

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A study of the fuel economy for various automobiles plotted the fuel consumption (liters used per 100 mi) vs speed (mph). A least-squares line was fit to the data. Here is the residual plot from this least-squares fit. What does the residual plot tell you about the linear model?

• The residual plot confirms the linearity of the fuel economy data.

• The residual plot does not confirm nor rule out the linearity of the fuel ecomomy data.

• The residual plot confirms a quadratic model is the best fit for the fuel economy data.

• The residual plot clearly indicates that the fuel ecomomy data isn't linear.

• A residual plot is not an appropriate means for evaluating a linear model.

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Leonardo da Vinci speculated that an ideal human would have an armspan that was equal to their height. Is it possible to predict armspan from height? The following computer regression printout shows the results of a least squares regression of armspan to height (both in inches) for a sample of 18 high school students. The students armspans' range from 62 to 76 inches. Which of the following statements is true?

• The correlation between height and armspan is .871

• A student who's height is 70" and armspan is 68" has a residual of -2.36".

• This regression model suggests that height is 84% of armspan.

• For a student 66" tall, this model would predict an armspan of 69".

• The coefficient of determination is 84%.

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