Exam 12: A: linear Regression and Correlation

In regression analysis, the independent variable is a variable whose value is known and is being used to explain or predict the value of another variable.

The prediction interval developed from a simple linear regression model will be very narrow when the value of x used to predict y is equal to the mean value .

In regression analysis, what do the residuals represent?

If the coefficient of determination is 0.975, then what may be said about the slope of the regression line?

Which of the following is measured by the coefficient of determination ?

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 0.

The value of the sum of squares for regression can never be smaller than 0.0.

A study of 20 students showed that the correlation between the time spent writing a test and the number of hours studied the night before the test was 0.35. Using a level of significance equal to 0.05, what does this imply?

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate will be 0.0.

A regression analysis between weight (y in kg) and height (x in cm) resulted in the following least-squares line: = -20 + 0.5x. Taking this into consideration, if the height is increased by 1 cm, what does this imply about the change in the weight, on average?

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least-squares line: = 75 +6x. From this information, if advertising is $800, then what is the predicted amount of sales (in dollars)?

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

In simple linear regression, one can use the plot of residuals versus the fitted values of y to check for a constant variance as well as to make sure that the linear model is in fact adequate.

Which of the following is 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)?

In order to predict with 98% 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-able values would be used?

A regression analysis between weight ( , in kg) and height ( , in cm) resulted in the following least-squares line: = -5 + 0.4 . This implies that if the height is increased by 1 cm, the weight is expected to increase by an average of 0.4 kg.

In a simple linear regression analysis, if SSE = 27, Total SS = 63, then what is the approximate percentage of the variation in the dependent variable y that is explained by the independent variable x?

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -0.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -0.85.

In simple linear regression, the plot of residuals versus fitted values can be used to check for which of the following

When all the points in a scatter diagram lie precisely on the estimated regression line, the sample coefficient of correlation will equal 0.