Exam 3: Describing Bivariate Data

If the correlation coefficient , then there is no linear relationship whatsoever between the dependent variable y and the independent variable x.

If two variables have a correlation coefficient equal to 0.005, this means that there is a strong relationship between the two variables.

Suppose that a regression line for a set of data has a y-intercept of 6.75 and a slope of 1.25. From this information, is it possible to determine the actual value of y when x = 2?

Which of the following would NOT be considered appropriate when constructing a scatterplot?

Which of the following values would be the correlation coefficient produced by a perfectly straight line sloping downward?

Legislation Poll A councillor was interested in determining whether people between the ages of 18 and 30 years of age would react to a piece of legislation differently than people over 30 years of age. The councillor polled a sample of 150 people from his district. The resulting data are shown in the table below: Reaction -Refer to the Legislation Poll table. Construct a side-by-side bar chart.

Students' GPA Narrative A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and . -Refer to Students' GPA Narrative. Interpret the correlation coefficient found in the previous question as to whether it could be used to predict students' GPAs after the first year. Justify your answer.

Weekly Amount Spent on Groceries Narrative The number of household members, x, and the amount spent on groceries per week, y, rounded to the nearest dollar, are measured for eight households in Lakehead area. The data are shown below: -Refer to Weekly Amount Spent on Groceries Narrative. Find the best-fitting regression line for these data.

Gasoline Prices and Fuel Efficiency Narrative. When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information: n = 7, ?x_i = 24.7, ?y_i = 177, ?x_iy_i = 600.7, s_x = 1.2406, and s_y=4.3861 -Refer to Gasoline Prices and Fuel Efficiency Narrative. Find the best-fitting line relating car engine size and fuel efficiency.

The scatterplot is a graph that is used to represent the relationship between two quantitative variables.

Gender Differences Narrative Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers, as shown below: -Refer to Gender Differences Narrative. Create a stacked bar chart to describe these data.

A manager of a supermarket wishes to show the relationship between the number of customers who come to the store on weekends and the total volume of sales (in dollars) during the same weekend. Which of the following graphs would likely be most useful if the manager has a sample of 52 weekends worth of data?

Selling Price and Age of Home Narrative A real estate agent is interested in knowing whether there is a relationship between the age of a house and the selling price. Listed below are the ages (in years) and selling prices (in $1000s) of a sample of six houses the agent has sold in the past year: -Refer to Selling Price and Age of Home Narrative. Based on the plot in the previous question, does there appear to be a relationship between the age of a house and selling price?

Given that 400, = 625, = 350, and n = 10, what is the correlation coefficient?

Meet Your Match Media Narrative The Executive Board of a popular online dating website, called Meet Your Match, wanted to know if there was a relationship between the age of a client and the number of persons they made contact with through the site. To find out, a random sample of 50 users from each of the 6 delineated age groups was drawn from its data base of active participants. The users were then surveyed as to how many persons had responded to the introduction email during the previous 3-month period. The average number of initial responses for each of the age groups was then recorded and organized into the following table. -Refer to Meet Your Match Media Narrative. What is the sample size?

Students' GPA Narrative A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's grade point average (GPA) after one year of law school. The administrator took a random sample of 15 students and computed the following summary information, where x = entrance exam score and y = GPA after one year: and . -Refer to Students' GPA Narrative. Find the correlation between the entrance exam score and the grade point average after one year of law school.

For which of the following tasks can the best-fitting regression line be used?