Exam 12: A: linear Regression and Correlation

In a simple linear regression , the following statistics are calculated from a sample of ten observations: = 2250, = 10, = 50, = 75. Which of the following values equals the least-squares estimates of the slope and y-intercept, respectively?

An automobile company in Ontario is interested in the relationship between the gender of its employees and employee productivity. A good starting point in this analysis would be to compute the coefficient of determination and the correlation coefficient.

In simple linear regression, if the estimated values and the corresponding actual values are equal, then the standard error of estimate, SE( ), must equal -1.0.

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.

If there is a negative correlation between the independent variable x and the dependent variable y, then to test this, the appropriate null and alternative hypotheses would be vs.

In developing an 80% prediction interval for the particular value of y from a simple linear regression involving a sample of size 12, the appropriate t-table value would be 1.372.

In order to predict with 95% confidence a particular value of for a given value of in a simple linear regression , a random sample of 20 observations is taken. The appropriate t-table value that would be used is 2.101.

Which of the following is the appropriate null hypothesis to test whether a population correlation is 0?

If the coefficient of determination value for a simple linear regression model is 0.90, then the correlation coefficient between the two variables will be 0.81.

Simple regression analysis is a statistical technique that establishes an index which provides, in a single number, a measure of the strength of association between two variables.

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.

In regression analysis, a graph of each residual against the corresponding fitted value is called a scatter diagram.

In simple linear regression, most often we perform a two-tailed test of the population slope to determine whether there is sufficient evidence to infer that a linear relationship exists. How should we state the null hypothesis? A) B) C) D)

If a simple linear regression model has no y-intercept, then which of the following may be deduced about the values of the variables?

In a simple linear regression , the following sums of squares are produced: , , and . What percentage of the variation in y may be explained by the variation in x?

A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least-squares line: = 80,000 + 5x. What does this imply?

If the sum of squares for error is equal to 0, then what must the coefficient of determination ( ) equal?

If a set of data contains no values of the independent variable x that are equal to 0, then the y-intercept regression coefficient has no particular meaning.

Given the least-squares regression line = -4.63 + 1.38x, and a coefficient of determination of 0.9025, what is the correlation coefficient?

Given the least-squares regression line = 5 -2x, what may be said about the relationship between the two variables?