Exam 12: Linear Regression and Correlation

The following are coefficients of correlation (r). The one that indicates a strong positive linear relationship between the two variables of interest is:

In a regression problem the following pairs of (x, y) are given: (4, 1), (4, -1), (4, 0), (4, -2) and (4, 2). That indicates that:

In developing a 90% confidence interval for the expected value of y from a simple linear regression problem involving a sample of size 15, the appropriate table value would be 1.761.

In order to predict with 90% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

Which of the following correctly describes a true regression line?

Which of the following is not an assumption for the simple linear regression model?

In regression analysis, if the coefficient of determination is 1.0, then:

If the coefficient of correlation is 0.90, then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

Which of the following correctly describes an estimated regression line?

Regression analysis is a statistical method that seeks to establish an equation that allows the unknown value of one variable to be estimated from the known value of one or more other variables.

A scientist is studying the relationship between x = inches of annual rainfall and y = inches of shoreline erosion. One study reported the following data. Use the following MINITAB output to answer the questions below. What is the equation of the estimated regression line? = ______________ Interpret the estimated slope of the regression line. ________________________________________________________ Is the simple linear regression model useful for predicting erosion from a given amount of rainfall? What is the p-value? ______________ Conclude: ______________ A linear relationship ______________ exist between x and y. The simple linear regression model ______________ useful for predicting erosion from a given amount of rainfall. Identify the coefficient of determination. ______________ Interpret the coefficient of determination. ________________________________________________________

If two variables are related in a negative linear manner, the scatterplot will show points on the x, y space that are generally moving from the upper left to the lower right.

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. Determine the standard error of estimate. s_r = ______________ Describe what this statistic tells you about the regression line. ______________ Determine the coefficient of determination. R² = ______________ Discuss what its value tells you about the two variables. ______________ Calculate the Pearson correlation coefficient. r = ______________ Why does it have the sign it has? ______________ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales. Test statistic: t = ______________ Rejection Region: Reject H₀ if | t | > ______________ Conclusion: ______________ A linear relationship ______________ between years of experience and sales.

A direct relationship is a relationship between any two variables, Y and X, such that the value of Y is uniquely determined whenever the value of X is specified (only Y exists for each X).

A measure of how well an estimated regression line fits the sample data on which it is based (denoted by and equal to the proportion of the total variation in the values of the dependent variable, y, that can be explained by the association of y with x as measured by the estimated regression line) is called the sample coefficient of correlation.

In regression analysis, the dependent variable is a variable whose value is unknown and is being explained or predicted with the help of another variable.

In a simple linear regression problem, the least squares line is = -3.75 + 1.25x, and the coefficient of determination is 0.81. The coefficient of correlation must be -0.90.

Testing whether the slope of the population regression line could be zero is equivalent to testing whether:

If a least squares regression line has a y-intercept of 6.84 and a slope of 2.16, then when x = 1 the actual value of y must be 9.

In regression analysis, the so-called regression line summarizes the stochastic relationship between dependent variable y and independent x, while also minimizing the errors made when the equation of that line is employed to estimate y from x.