Exam 3: Describing Bivariate Data

The best fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself.

If two variables have a correlation coefficient equal to 0.005, this means that there is no relationship between the two variables.

If the correlation coefficient between the independent variable x and the dependent variable y is 0.87, then the best fitting line would have a slope equal to 0.87.

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 the Big Rapids area. The data are shown below: Create a raw scatterplot of these eight data points (no regression line or equation). Find the best-fitting regression line for these data. y = ______________ Plot the points and the best-fitting line on the same graph. 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? ________________________________________________________

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 Find the correlation between the entrance exam score and the grade point average after one year of law school. ______________ Interpret the correlation coefficient found in part (a). ____________________________ Find the best fitting line relating grade point average after on year of law school and score on the entrance exam. y = ______________ 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? ______________

The best-fitting regression line can be used to:

In constructing a scatterplot, it would not be appropriate to:

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

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

Given the least squares regression line y = 3.8 - 2x,

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

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.

A scatterplot can be used to determine the relationship between:

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be:

If a regression line has a y-intercept of 6.75 and a slope of 1.25, then when x = 2 the actual value of y is: