Exam 12: A: linear Regression and Correlation

A sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525. What is the test statistic value for testing vs.

In a simple linear regression analysis, which of the following best describes the standard error of the slope?

The residuals are observations of the error variable . Consequently, the minimized sum of squared deviations is called the sum of squares for error.

Which of the following is an indication of no linear relationship between two variables x and y?

When regression analysis is used for prediction, the confidence interval for the average y given x will be wider than the prediction interval for a particular value of y given x.

The regression model = 36.5 + 20.1x has been computed based on a sample of 50 observations. One observation in the sample was (x, y) = (14, 350.9). Given this, the residual value for this observation is 33.

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate will be -1.0.

In a simple linear regression model, the regression slope coefficient will have the same sign as the correlation coefficient.

The values of a and b found in the equation of the estimated regression line represent the line's y-intercept and slope, respectively, and are called estimated regression coefficients.

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

The sign of the correlation coefficient in a simple linear regression model will always be the same as the sign of the y-intercept coefficient .

In a simple linear regression model, testing whether the slope of the population regression line could be 0 is the same as testing whether or not the population coefficient of correlation equals 0.

If all of the values of an independent variable x are equal, then regressing a dependent variable y on this independent variable x will result in which of the following coefficients of determination ( )?

In regression analysis, if the coefficient of determination is 1.0, which of the following statements can be deduced from this information?

In developing a 90% confidence interval for the average value of y from a simple linear regression involving 12 observations, the appropriate t-table value would be 1.796.

In publishing the results of some research work, the following values of the correlation coefficient were listed. Which one is incorrect?

In a simple linear regression , if the sum of squares for regression is 90, then the total sum of squares is at least 90.

In a simple linear regression , the least-squares line is = 2.73 - 1.02 , and the coefficient of determination is 0.7744. The correlation coefficient must be -0.88.

The values of α and found in the equation of the true regression line E(y) = represent the line's y-intercept and slope, respectively, and are called true regression coefficients.

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.