Exam 3: Describing Bivariate Data

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. If a student scored 91 on the entrance exam, what would you predict the student's grade point average to be after one year of law school?

When constructing a scatterplot, the independent variable x is placed on the horizontal axis, and the dependent variable y is placed on the vertical axis.

A perfectly straight line sloping upward would produce a covariance value of +1.

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 are the two primary variables of interest in this experiment? Are they qualitative or quantitative?

Soft Drink Sales Narrative A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in 1000s of cases. She compiled the figures for 20 weeks and computed the following summary information: n = 20, and . -Refer to Soft Drink Sales Narrative. If the soft drink distributor ran 21 TV ads per week for her product, what would you predict her sales to be?

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 Selling Price and Age of Home Narrative. Plot the data on a scatterplot.

Generally speaking, if two quantitative variables are unrelated, the covariance will be a positive or negative number close to zero.

The standard deviation is a measure of the linear relationship between two quantitative variables.

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. What would you estimate a household of seven to spend on groceries per week? Should you use the fitted line to estimate this amount? Why or why not?

The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable x.

If all the points in a scatterplot lie on the least squares regression line, then what must the correlation coefficient r be?

Which of the following is NOT a measure of the linear relationship between two 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. Which of the charts created in the above three questions best depicts the difference or similarity of the responses of men and women? Give reasons for your answer.

A scatterplot can be used to depict the relationship between which kinds of variables?

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 correlation between engine size and fuel efficiency.

If the correlation coefficient , then all the data points lie exactly on a straight line.

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 pie chart for each of the age groups.

A perfectly straight line sloping downward would produce a covariance value of -1.

If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane moving generally from the lower left corner to the upper right corner.

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. Plot the points and the best-fitting line on the same graph.