Exam 14: Correlation and Regression.

A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT)and performance on an anagram task.(Anagrams are words with the letters scrambled.The task is to unscramble the letters and identify the word.)Each subject is given a set of 10 anagrams,and the psychologist records how much time is needed to solve all 10.The anagram times and each subject's SAT score are as follows.(Note that two subjects failed to complete all 10 anagrams.)Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance. Aubject Time SAT Score 1 104 480 2 195 410 3 50 590 4 93 510 5 failed 420 6 170 460 7 failed 380 8 67 570 9 45 640 10 58 600

For a regression equation with a positive slope,if the X value is above the mean for the X scores,then the predicted Y value will be above the mean for the Y scores.

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?

A researcher measures IQ and weight for a group of college students.What kind of correlation is likely to be obtained for these two variables?

A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right.

A set of X and Y scores has SSₓ = 10,SSʏ = 36,and SP = 20.The regression equation for these scores will have a slope constant of 2.

Suppose that a sample of n = 12 pairs of X and Y scores has SS? = 90 and a Pearson correlation of r = +0.40. a.What proportion of the variance for the Y scores is predicted by the regression equation? b.Does the regression equation predict a significant portion of the variance? Test with ? = .05.

A set of n = 5 pairs of X and Y values has SSₓ = 16,SSʏ = 4 and SP = 2.For these data,what is the Pearson correlation?

As the sample size gets larger,what happens to the size of the correlation that is needed for significance?

For the regression equation Ŷ = -2X + 6,what can be determined about the correlation between X and Y?

For the linear equation Y = 2X - 3,which of the following points will not be on the line?

The sign of the correlation (+/-)is generally meaningless for the point-biserial correlation and the phi-coefficient.

If the Pearson correlation between X and Y is r = 0.60,then the regression equation predicts 36% of the variance in the Y scores.

In a test for significance of a Pearson correlation for a sample of n = 30 individuals,you determine the critical value by using df = 29.

For linear regression,the value of SSᵣₑsᵢdᵤₐl can be computed directly by Σ(Y -Ŷ)².

If the Spearman correlation for a set of scores is equal to +1.00,then the Pearson correlation for the same scores would also be equal to +1.00.

The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1,9.

For the data below: a.Find the regression equation for predicting Y from X. b.Calculate the predicted Y for each X value, find each residual (Y - Ŷ), square each residual and add the squared values to obtain SSᵣₑsᵢdᵤₐl. 5 10 3 6 6 7 4 3 2 4

Suppose the correlation between height and weight for adults is +0.40.What proportion (or percent)of the variability in weight can be explained by the relationship with height?

If you measured hearing acuity and age for a group of people who are 50 to 90 years old,you should obtain a positive correlation between the two variables.