must answer them correctly! please

Checkpoint: Examining Relationships: Quantitative Data

Question 1

Select one answer.

10 points

Pre-Statistics and Statistics Course Grades: We recorded the pre-statistics course grade (in percent) and introductory statistics course grade (in percent) for 60 community college students. Then we generated the following scatterplot of the data.

For this linear regression model, r² = 0.70. What does this mean?

Question 2

Select one answer.

10 points

Pre-Statistics and Statistics Course Grades: We recorded the pre-statistics course grade (in percent) and introductory statistics course grade (in percent) for 60 community college students. The standard error s_e for the linear regression model that predicts introductory statistics course grades using pre-statistics course grades (predicted introductory statistics course grade = -0.147 + 0.9810 (pre-statistics grade)) is about 4.5%. In terms of estimating introductory statistics course grades, what does this mean?

Question 3

Select one answer.

10 points

 

Which one of the four scatterplots above shows two variables with a strong negative linear association?

Question 4

Select one answer.

10 points

Influential outlier: The correlation coefficient for the scatterplot above is r = −0.72. The point (17, 21) appears to be an outlier since it doesn’t follow the general pattern of the data, so we want to determine how much it influences the value of r. To do this, we remove the outlier from the data set and recalculate r.

How does the value of r change?

Question 5

Select one answer.

10 points

A scientist studies how fast a ball will fall when dropped from a height. He drops a ball from different heights and measures the time it takes the ball to reach the ground.

Below is the scatterplot of times and heights that he finds, along with the regression line. Next to the scatterplot is a plot of the residuals. The correlation between heights and times is about 0.98.

Does the regression line summarize the pattern for these data?

Question 6

Select one answer.

10 points

Match the scatterplot: Which of the four scatterplots below matches the following description: “For our class, we observed that there is a weak negative linear association between the average number of hours a student works per week and the student’s overall exam average”?

Question 7

Select one answer.

10 points

Which one of the four scatterplots below shows a relationship with a strong curvilinear pattern?

  

Question 8

Select one answer.

10 points

Match the scatterplot: Which scatterplot has a correlation coefficient of -0.85?

Question 9

Select one answer.

10 points

For a linear regression model with standard error s_e, why would you want a small s_e in your model?

Question 10

Select one answer.

10 points

Videogame data: We collected data on the top 50 best-selling video games. These are the variable descriptions:

Metascore: Score out of 100, based on major critic reviews as provided by Metacritic.com

Total Worldwide Sales: Total number copied sold worldwide since December 31, 2015.

GameRankings: Score out of 100%, based on an average scores from websites and magazine reviews.

We used Metascore ratings as an explanatory variable and GameRankings ratings as the response variable in a linear regression. The r² value is 48%. With Total Worldwide Sales as the explanatory variable and GameRankings ratings as the response variable in a linear regression, the r² value is 62%. Using the r² value, which is a better predictor of a videogames’s GameRankings score: Metascore or Total Worldwide Sales?

Question 11

Select one answer.

10 points

The scatterplot below shows Olympic gold medal performances in the long jump and the high jump from 1900 to 1988. Each point shows the long jump distance that won the gold medal and also the height that won the high jump for the same year. The correlation between the two kinds of jumps is 0.89.

What would be a reasonable explanation for this high correlation?

Question 12

Select one answer.

10 points

Math workshops and final exams: The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy.

Which is the explanatory variable?

Question 13

Select one answer.

10 points

The scatterplot below includes the least-squares regression line for predicting the average daily number of new savings accounts based on the interest rate.

Which equation is a reasonable description of the least-squares regression line for the Predicted Average Daily Number of New Savings Accounts? (Note: a rate of 2.05% would be entered into the model as "2.05.")

Question 14

Select one answer.

10 points

If the correlation coefficient for a given scatterplot is r = 0.73, which of the following must be true about the relationship between the explanatory and response variable?

Question 15

Select one answer.

10 points

Pre-Statistics and Statistics Course Grades: We recorded the pre-statistics course grade (in percent) and introductory statistics course grade (in percent) for 60 community college students.

The linear regression equation is:

Predicted introductory statistics course grade = - 0.147 + 0.981 (Pre-statistics course grade)

What does the slope of the regression line tell us?

Question 16

Select one answer.

10 points

Pre-Statistics and Statistics Course Grades: We recorded the pre-statistics course grade (in percentage) and introductory statistics course grade (in percentage) for 60 community college students.

Suppose a struggling student who is currently taking pre-statistics and not passing (60%) wants to predict his introductory statistics course grade. Should the regression line be used for this prediction?

Question 17

Select one answer.

10 points

Airfare prices: Suppose that we want to examine the relationship between distance (in miles) and the cost of round-trip airfare from LAX (Los Angeles International Airport). We collect data from a travel search engine. The linear regression equation is

Predicted round-trip airfare = 146.2 + 0.1442 (distance)

The round-trip airfare to fly between LAX and San Francisco is $174, and the distance traveled is 382 miles. What is the residual related to this flight itinerary?

Question 18

Select one answer.

10 points

Pre-Statistics and Statistics Course Grades: We recorded the pre-statistics course grade (in percent) and introductory statistics course grade (in percent) for 60 community college students.

In this data set, no one earned a 90% for the pre-statistics course grade. How could you estimate a student’s introductory statistics course grade if she earned 90% for the pre-statistics course grade?

Question 19

Select all that apply.

10 points

Which of the following statements is true of a least-squares regression line? Check all that apply.

Question 20

Select one answer.

10 points

Movie data: We collected data from IMDb.com on 70 movies listed in the top 100 US box office sales of all time. These are the variable descriptions:

Metascore: Score out of 100, based on major critic reviews as provided by Metacritic.com

Total US box office sales: Total box office sales in millions of dollars

Rotten Tomatoes: Score out of 100, based on authors from writing guilds or film critic associations

We used Metascore ratings as an explanatory variable and Rotten Tomato ratings as the response variable in a linear regression. The s_e value is 11. With US box office sales as the explanatory variable and Rotten Tomato ratings as the response variable in a linear regression, the s_e value is 22. Using the s_e value, which is a better predictor of a movie’s Rotten Tomatoes score: Metascore or total US box office sales?