AP Statistics (Chapter 3)

A ______ association is defined when above average values of one variable are accompanied by below average values of the other.

Negative

2. If two variables are positively associated, then (A) larger values of one variable are associated with larger values of the other. (B) larger values of one variable are associated with smaller values of the other. (C) smaller values of one variable are associated with larger values of the other. (D) smaller values of one variable are associated with both larger/smaller values of the other. (E) there is no pattern in the relationship between the two variables.

(A) larger values of one variable are associated with larger values of the other.

11. Which of the following statements concerning residual from a LSRL is true? (A) The sum of the residuals is always 0. (B) A plot of the residuals is useful for assessing the fit of the least-squares regression line. (C) The value of a residual is the observed value of the response minus the value of the response that one would predict from the least-squares regression line. (D) An influential point on a scatterplot is not necessarily the point with the largest residual. (E) All of the above.

(E) All of the above.

3. The correlation coefficient measures (A) whether there is a relationship between two variables. (B) the strength of the relationship between two quantitative variables. (C) whether or not a scatterplot shows an interesting pattern. (D) whether a cause and effect relation exists between two variables. (E) the strength of the linear relationship between two quantitative variables.

(E) the strength of the linear relationship between two quantitative variables.

The use of a regression linnet make a prediction far outside the observed X values.

Extrapolation

The _____-_______ regression line is also known as the line of best fit.

Least-Squares

The coefficient of _________ describes the fraction of variability in Y values that is explained by least squares regression on X.

Determination

The ________ of a scatterplot indicates a positive or negative association between the variables.

Direction

The ____ of a scatterplot is usually linear or nonlinear.

Form

Individual points that substantially change the correlation or slope of the regression line.

Influential

An individual value that falls outside the overall pattern of the relationship.

Outlier

A _________ association is defined when above average values of the response.

Positive

Y-hat is the __________ value of the y-variable fora given X.

Predicted

Line that describes the relationship between two quantitative variables.

Regression

The difference between an observed value of the response and the value predicted by a regression line.

Residual

Variable that measures the outcome of a study.

Response

Graphical display of the relationship between two quantitative variables.

Scatterplot

The amount by which Y is predicted to change when X increases by one unit.

Slope

The _______ of a relationship in a scatterplot in a scatterplot is determined by how closely the point follow a clear form.

Strength

6. If another data point were added with an air temperature of 0°C and a stopping distance of 80 feet, the correlation would (A) decrease, since this new point is an outlier that does not follow the pattern in the data. (B) increase, since this new point is an outlier that does not follow the pattern in the data. (C) stay nearly the same, since correlation is resistant to outliers. (D) increase, since there would be more data points. (E) Whether this data point causes an increase or decrease cannot be determined without recalculating the correlation.

(A) decrease, since this new point is an outlier that does not follow the pattern in the data.

7. Which of the following is true of the correlation? (A) It is a resistant measure of association. (B) -1≤ r ≤ 1. (C) If r is the correlation between X and Y, then -r is the correlation between X and Y. (D) Whenever all the data lie on a perfectly straight line, the correlation r. (E) All of the above.

(B) -1≤ r ≤ 1.

15. A study gathers data on the outside temperature during the winter in degrees Fahrenheit and the amount of natural gas a household consumes in cubic feet per day. Call the temperature X and gas consumption Y. The house is heated with gas, so X helps explain Y. The least-squares regression line for predicting Y from X is: y^ = 1344 - 19x. When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line? (A) It goes up 19 cubic feet. (B) It goes down 19 cubic feet. (C) It goes up 1344 cubic feet. (D) It goes down 1344 cubic feet. (E) Can't tell without seeing the data.

(B) It goes down 19 cubic feet.

1. A study is conducted to determine if one can predict the academic performance of a first-year college student based on their high school grade point average. The explanatory variable in this study is (A) academic performance of the first year student. (B) grade point average. (C) the experimenter. (D) number of credits the student is taking. (E) the college.

(B) grade point average.

4. Consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Centigrade) for a certain 2,000-pound car traveling 40 mph. *Scatterplot is only available in the book (pg. 53) - Do these data provide strong evidence that warmer temperatures actually cause a greater stopping distance? (A) Yes. The strong straight-line association in the plot shows that temperature has a strong effect on stopping distance. (B) No. r ≠ 1 (C) No. We can't be sure the temperature is responsible for the difference in stopping distances. (D) No. The plot shows that differences among stopping distances are not large enough to be important. (E) No. The plot shows that stopping distances go down as temperature increases.

(C) No. We can't be sure the temperature is responsible for the difference in stopping distances.

14. A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. The study found that children who watch more television tend to have lower reading scores than children who watch fewer hours of television. The study report says that "Hours of television watched explained 25% of the observed variation in the reading scores of the 125 subjects." The correlation between hours of TV and reading score must be (A) r = 0.25 (B) r = -0.25 (C) r = -0.5 (D) r = 0.5 (E) Can't tell from the information given.

(C) r = -0.5

5. If stopping distance was expressed in yards instead of feet, how would the correlation r between temperatures and stopping distance change? (A) r would be divided by 12. (B) r would be divided by 3. (C) r would not change. (D) r would be multiplied by 3. (E) r would be multiplied by 12.

(C) r would not change.

8. Consider the following scatterplot of CO (carbon monoxide) and NOX (nitrogen oxide) in grams per mile driven in the exhausts of cars, The least squares regression line has been drawn in the plot. *Scatterplot is only available in the book (pg. 54) - Based on the scatterplot, the least-squares line would predict that a car that emits 2 grams of CO per mile driven would emit approximately how many grams of NOX per mile driven? (A) 4.0 (B) 1.25 (C) 2.0 (D) 1.7 (E) 0.7

(D) 1.7

13. What percent of variability in the number of eggs is explained by the least-squares regression of number of eggs on fish length? *This question relates to question 12. (A) 25.55 (B) 5.392 (C) 6.75133 (D) 69.7 (E) Cannot be determined without the original data.

(D) 69.7

10. Which of the following is correct? (A) The correlation r is the shape of the least-squares regression line. (B) The square of the correlation is the slope of the least-squares regression line. (C) The square of the correlation is the population of the data lying on the least-squares regression line. (D) The coefficient of determination is the fraction of variability in y that can be explained by least-squares regression of y and x. (E) The sum of the squared residuals from the least-squares line is 0

(D) The coefficient of determination is the fraction of variability in y that can be explained by least-squares regression of y and x.

12. A fisheries biologist studying whitefish in a Canadian lake collected data on the length (in centimeters) and egg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. Note that the Number of eggs is given in thousands (i.e., "40" means 40,000 eggs). *Scatterplot is only available in the book (pg. 55) - Which of the following statements is a correct interpretation of the slope of the regression line? (A) For each 1-cm increase in the fish length, the predicted number of eggs increases by 39.25. (B) For each 1-cm increase in the fish length, the predicted number of eggs decreases by 142.74 (C) For each 1-cm increase in the number of eggs, the predicted fish length increases by 39.25cm. (D) For each 1-cm increase in the number of eggs, the predicted fish length decreases by 142.74cm. (E) For each 1-cm increase in the fish length, the predicted number of eggs increases by 39,250.

(E) For each 1-cm increase in the fish length, the predicted number of eggs increases by 39,250.

Variable that may help explain or influence changes in another variable.

Explanatory

Important note: Association does not imply _____________.

Causation

Value that measures the strength of the linear relationship between two quantitative variables.

Correlation