Unit 2 MCQ - 2 Variable Statistics

The following is a residual plot for a linear regression of y versus x. What is indicated by the plot?

B A linear model is not appropriate.

The following bar chart displays the relative frequency of responses of students, by grade level, when asked, "Do you volunteer in a community-service activity?" Which of the following statements is not supported by the bar chart?

D The number of tenth-grade students who responded yes was greater than the number of ninth-grade students who responded yes.

A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output. Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?

A 30

Which of the following is the best description of a positive association between two variables?

As the value of one of the variables increases, the value of the other variable tends to increase.

The following data were collected from a random sample of people, who identified their favorite type of juice. The results are shown in the following two-way table. What proportion of the children identified orange as their favorite type of juice?

B 400/700

A set of bivariate data was used to create a least-squares regression line. Which of the following is minimized by the line?

B The sum of the squared residuals

A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height?

B There is no linear relationship between time and height.

A split ticket is a voting pattern in which a voter casts votes for candidates from more than one political party. In a recent study, 1,000 men and women were asked whether they voted a split ticket in the last election. The totals are shown in the following table. What value of "a" would indicate no association between gender and voting pattern for the people in the sample?

C 480

The relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln⁡(y^)=7−0.045x, where x represents the fuel efficiency, in miles per gallon, and y^ represents the predicted carbon dioxide emissions, in grams per mile. Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon?

C 446

Researchers observed the grouping behavior of deer in different regions. The following scatterplot shows data collected on the size of the group and the percent of the region that was woodland. The relationship between group size and percent woodland appears to be negative and nonlinear. Which of the following statements explains such a relationship?

C As the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.

Which of the following statements about a least-squares regression analysis is true? I. A point with a large residual is an outlier. II. A point with high leverage has a y-value that is not consistent with the other y-values in the set. III. The removal of an influential point from a data set could change the value of the correlation coefficient.

C I and III only

The following segmented bar chart shows the number of flights that were either on time or delayed at three different airports on one day. Which of the following statements is supported by the bar chart?

C The number of on-time flights at Airport S is half the number of on-time flights at Airport T.

A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?

C The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant.

For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?

D No, because 3 inches falls above the maximum value of lengths in the sample.

An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot?

D There should be no pattern in the residual plot.

In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively. Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?

E E

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

E Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

A researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age. Does the residual plot support the appropriateness of a linear model?

E No, because the graph displays a U-shaped pattern.

A family would like to build a linear regression equation to predict the amount of grain harvested per acre of land on their farm. They subdivide their land into several smaller plots of land for testing and would like to select an explanatory variable they can control. Which of the following is an appropriate explanatory variable that the family could use to create a linear regression equation?

E The amount of fertilizer applied to each plot of land

The height ℎ and collar size c, both in centimeters, measured from a sample of boys were used to create the regression line c^(hat)=−94+0.9ℎ. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?

E The c-intercept of the regression line