Question

# 9. A lot of corn grows in Iowa. For several years, farmers have kept track of...

9. A lot of corn grows in Iowa. For several years, farmers have kept track of the amount of rainfall (in inches) and the amount of corn produced (in bushels per acre). A strong and linear relationship has been observed between these variables. When a regression equation is constructed in order to predict amount of corn produced based on rainfall, it is found that the equation has an intercept of 89.54 and a slope of 0.13. We can conclude from this information that as rainfall increases by 1 inch, amount of corn produced is predicted to change by

A. 1 bushel per acre

B. 0.13 bushels per acre

C. 89.54 bushels per acre

D. This question cannot be answered without seeing the full regression equation.

E. This question cannot be answered without knowing the exact value of the correlation coefficient.

10. You have gathered data from a random sample of 125 3rd grade students in order to better understand how amount of television watched per week (in hours) relates to reading test scores. Your ultimate goal is to construct a regression equation to predict reading test scores based on amount of television watched per week. If this is your goal, which variable should you put on the horizontal axis of a scatterplot of this data?

A. Hours of television, because it is the response variable.

B. Hours of television, because it is the explanatory variable.

C. Reading score, because it is the response variable.

D. Reading score, because it is the explanatory variable.

E. When conducting a regression analysis, it makes no difference which variable is on which axis.

11. A study is done of students commuting to a large university by bicycle. The correlation between the time spent waiting at traffic lights and total cycling time is 0.50. This means that:

A. The average rider spent half her cycling time waiting at traffic lights.

B. The more time a rider spends waiting at traffic lights, the higher the total cycling time is likely to be.

C. If the rider's time at traffic lights increases by 5 minutes, she will spend an additional 10 minutes commuting, on average.

D. If the rider's time at traffic lights increases by 10 minutes, she will spend an additional 5 minutes commuting, on average.

12. As the speed (in miles per hour) of an automobile increases, the gas mileage (in miles per gallon) first increases and then decreases. Suppose that this relationship is very regular, as shown by the following data table and scatterplot.

 Speed 30 40 50 60 70 Mileage 20 24 26 24 20

​Why would we not want to compute a correlation coefficient (r) with this data set?

A. The sample size is too small.

B. The variables are on the wrong axes; speed should be on the y-axis and mileage should be on the x-axis.

C. The relationship is not linear.

D. We don’t know if one variable causes the other.

E. We have the wrong kind of data; we need one quantitative variable and one categorical variable to compute a correlation coefficient.

13. An educational researcher gathers data from students at an elementary school and observes that there is a negative and linear relationship between the number of hours spent playing video games per week and the number of hours spent working on homework per week. When a regression equation is constructed to predict hours spent working on homework based on hours spent playing video games, it is observed that r2 = 68%. This means that r must be equal to

A. -0.34.

B. -0.68

C. -0.82.

D. -0.08.

E. None of the above.

beacuse linear regression is

corn produced =89.54 + 0.13 * Rainfall

If.rainfall increases by 1 inch, amount of corn produced is predicted to change by 0.13.

Hours of television, because it is the explanatory variable.

Answer(11)option A. The average rider spent half her cycling time waiting at traffic lights.

Answer(12) option C. The relationship is not linear.

because negative realtionship and R=sqrt(R^2)=sqrt(.68)=.824 therefore R value = -0.82