Exam 12: A: linear Regression and 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 regression setting, which of the following is NOT an assumption about the random error, ?

In a simple linear regression model, if the regression slope coefficient is negative, then the standard error of the estimate will be positive.

In a regression the following pairs of (x, y) are given: (4, 1), (4, -1), (4, 0), (4, -2) and (4, 2). Which of the following statements may be deduced from the given information?

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

In the least-squares regression line = 3 - 2x, which of the following is the correct predicted value of y?

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

If the true correlation between two variables is 0, then there is no linear relationship between the two variables.

If an estimated regression line has a y-intercept of 10 and a slope of 4, then when x = 2 what is the actual value of y?

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the sum of squares for error will be negative also.

In developing a simple linear regression model, only one independent variable is used to explain the variation in a single dependent variable.

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

In a simple linear regression model, if you found that the true regression coefficient is significantly greater than 0, then you may also conclude that the two variables are positively correlated.

Which of the following correctly describes a true regression line?

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be positively related, then the sign of the slope regression coefficient will be positive also.

If the coefficient of determination is 0.982, then the slope of the regression line must be positive.

The method of least-squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

Given that the sum of squares for error is 52 and the sum of squares for regression is 148, then the coefficient of determination is 0.74.

In a simple linear regression model, if the regression model is statistically significant, then the regression slope coefficient is significantly greater than 0.

In a simple linear regression model, the slope coefficient represents the average change in the independent variable x for a one-unit change in the dependent variable y.