Lesson 2.7 Checkpoint

More students are taking statistics in high school than ever before. One way to track this trend is to look at the number of AP® Statistics exams given each year. A linear model was used to predict y = number of AP® Statistics exams from x = year. Here is the residual plot for that model.

Use it to determine if the regression model is appropriate. (LT 2.7.1 #1)

• Because there is a leftover pattern in the residual plot, the least-squares regression line is not an appropriate model for the relationship.

• Because there is a leftover pattern in the residual plot, the least-squares regression line is an appropriate model for the relationship.

• Because there is no leftover pattern in the residual plot, the least-squares regression line is not an appropriate model for the relationship.

• Because there is no leftover pattern in the residual plot, the least-squares regression line is an appropriate model for the relationship.

Mac and Nick collected data from a random sample of students at their school to see if they could use a linear model to predict y = a student’s grade point average from x = the number of text messages a student sent on the previous day. Here is the residual plot for that model.

Use it to determine whether the regression model is appropriate. (LT 2.7.1 #2)

• Because there is a leftover pattern in the residual plot, the least-squares regression line is not an appropriate model for the relationship.

• Because there is a leftover pattern in the residual plot, the least-squares regression line is an appropriate model for the relationship.

• Because there is no leftover pattern in the residual plot, the least-squares regression line is not an appropriate model for the relationship.

• Because there is no leftover pattern in the residual plot, the least-squares regression line is an appropriate model for the relationship.

A random sample of 195 students was selected from the United Kingdom. The scatterplot shows the relationship between y = height (in centimeters) and x = age (in years), along with the least-squares regression line. The standard deviation of the residuals for this model is s = 8.61. Interpret this value. (LT 2.7.2 #1)

• The actual height is typically about 8.61 cm away from its predicted height using the least-squares regression line with x = age (in years).

• The actual height is 8.61 cm away from its predicted height using the least-squares regression line with x = age (in years).

• The actual age is typically about 8.61 years away from its predicted age using the least-squares regression line with x = height (in cm).

• You can't interpret s.

Joan keeps a record of the natural gas that her furnace consumes for each month from October to May. The following scatterplot shows the relationship between x = average temperature (in degrees Fahrenheit) and y = average gas consumption (in cubic feet per day) for each month, along with the least-squares regression line. The standard deviation of the residuals for this model is s = 46.4.

Interpret this value. (LT 2.7.2 #2)

• The actual average gas consumption is typically about 46.4 cubic feet per day away from its predicted average gas consumption using the least-squares regression line with x = average temperature (in F).

• The actual average gas consumption is 46.4 cubic feet per day away from its predicted average gas consumption using the least-squares regression line with x = average temperature (in F).

• The actual average temperature is typically about 46.4 F from its predicted average temperature using the least-squares regression line with x = average gas consumption (cubic feet per day)

• You can't interpret s.

A random sample of 195 students was selected from the United Kingdom. The scatterplot shows the relationship between y = height (in centimeters) and x = age (in years), along with the least-squares regression line. The value of r² for the linear model relating y = height (in centimeters) to x = age (in years) is r² = 0.274. Interpret this value. (LT 2.7.3 #1)

• 27.4% of the variability in height is accounted for by the least-squares regression line with x = age (in years).

• 27.4 of the variability in height is accounted for by the least-squares regression line with x = age (in years).

• 0.274% of the variability in height is accounted for by the least-squares regression line with x = age (in years).

• 0.274 of the variability in height is accounted for by the least-squares regression line with x = age (in years).

Joan keeps a record of the natural gas that her furnace consumes for each month from October to May. The following scatterplot shows the relationship between x = average temperature (in degrees Fahrenheit) and y = average gas consumption (in cubic feet per day) for each month, along with the least-squares regression line. The value of r² for the linear model relating y = average gas consumption (in cubic feet per day) and x = average temperature is r² = 0.966. Interpret this value. (LT 2.7.3 #2)

• 96.6% of the variability in average gas consumption is accounted for by the least-squares regression line with x = average temperature (in degrees Fahrenheit).

• 96.6 of the variability in average gas consumption is accounted for by the least-squares regression line with x = average temperature (in degrees Fahrenheit).

• 0.966 of the variability in average gas consumption is not accounted for by the least-squares regression line with x = average temperature (in degrees Fahrenheit).

• 0.966 of the variability in average gas consumption is accounted for by the least-squares regression line with x = average temperature (in degrees Fahrenheit).