Exam 12: Linear Regression and Correlation

In (all types of) regression analysis, a variable whose value is known and is being used to explain or predict the value of another variable is called:

If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination ( ) must be:

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 zero.

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 regression analysis, if the values of the dependent variable, y, decrease with larger values of the independent variable, x, the variables are said to have:

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 a simple linear regression model has no y-intercept, then:

In a simple linear regression setting, the deterministic model equation determines an exact value of the dependent variable y when the value of the independent variable x is given, since all points must lie exactly on the line.

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.

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

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.

In order to predict with 99% 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?

A scientist is studying the relationship between wind velocity (x) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. What is the least squares regression line? = ______________ Predict the DC output for a wind velocity of 22 mph. ______________ What is the value of the error sum of squares? ______________ One of the assumptions about the random error in the regression model is that the values of have a common variance equal to . What is the best estimator of ? ______________ What is the coefficient of determination? ______________ Does a linear relationship exist between x and y? Test using = 0.05. What is the p-value? ______________ Conclude: ______________ A linear relationship ______________ exist between x and y.

The value of the sum of squares for regression SSR can never be smaller than 1.

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

In regression analysis we use the Spearman rank correlation coefficient to measure and test to determine whether a relationship exists between the two variables if:

In order to estimate with 95% 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?

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.

In a simple linear regression analysis, if the t-test statistic for testing the significance of the regression model is 3.4, then the F-test statistic from the ANOVA table for regression will be 11.56.

A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. Find the correlation coefficient. r = ______________ There is ______________ linear relationship between x and y.