Exam 12: A: linear Regression and Correlation

If there is no linear relationship between two variables and , the coefficient of determination must be 1.0.

A regression analysis between sales (y in $1000) and advertising (x in $100) resulted in the following least-squares line: = 82 + 7x. Given this information, if advertising costs were $900, what could we reasonably expect the amount of sales (in dollars) to be?

In developing a 95% confidence interval for the expected value of y from a simple linear regression involving a sample of size ten, the appropriate critical value would be 1.86.

Which of the following correctly describes an estimated regression line?

A large coefficient of determination value will result in a small standard error of the estimate for the regression model, thus providing prediction intervals that are narrow.

In a simple linear regression , if the coefficient of determination is 0.96, what does this imply?

The confidence interval estimate of the expected value of y will be wider than the prediction interval for the same given value of x and confidence level. This is because there is more error in estimating a mean value as opposed to predicting an individual value.

Testing whether the slope of the population regression line could be 0 is equivalent to testing which of the following?

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

In regression analysis, a careful study of the differences between observed and estimated y values, given x (in order to decide whether crucial assumptions are fulfilled that allow valid inferences about the true regression line to be made from an estimated regression line) is called residual analysis.

The value of the sum of squares for regression can never be larger than 100.

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 order to predict with 99% confidence the expected value of y for a given value of x in a simple linear regression , a random sample of ten observations is taken. Which of the following t-table values would be used?

In a simple linear regression , if the sum of squares for regression is 90, then the correlation coefficient is 0.9.

In developing a 90% prediction interval for the particular value of y from a simple linear regression involving a sample of size 14, the appropriate t-table value would be 2.179.

One way to measure the strength of the relationship between the response variable y and the predictor variable x is to calculate the coefficient of determination, that is, the proportion of the total variation in y that is explained by the linear regression of y on x.

What is the symbol for the population coefficient of correlation?

In a simple linear regression analysis, it was stated that the correlation between starting salary and years of experience is 0.80. This indicates that 80% of the variation in starting salary is explained by years of experience.

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression , a random sample of 15 observations is taken. Which of the following t-table values would be used?

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least-squares line: = 77 + 8x. This implies that if advertising is $600, then the predicted amount of sales is $125,000.