Exam 13: Pearson Correlation and Regression: Inferential Aspects

Imagine you are interested in researching the relationship between job experience and income among early-career working professionals.You take a random sample of 32 professionals from the nearest city,and you ask them to report their annual income and submit a resumé outlining their professional experience.You later calculate their years of experience from their resumés.You compute the following information: If you were to calculate a 95% confidence interval for this correlation coefficient,you would find that it ranges from .11 to .70.How should this interval be interpreted?

Based on the Applications to the Analysis of Social Problems section of Chapter 14,a smoothing technique

The assumption that the population distributions of X and Y are such that their joint distribution (that is,their scatterplot)represents a bivariate normal distribution implies that the distribution of Y scores at any value of X is normal in the population.

When r ¹ 0,the sampling distribution of r is normal in shape.

If an experimental research strategy was used (i.e.,random assignment and control of extraneous variables),then causality can be inferred from a statistically significant correlation.

r₂ is formally known as ____________________.

Discuss the robustness of Pearson correlation.

Which of the following is formally known as the coefficient of determination?

We can test the null hypothesis that ñ = 0 by transforming the sample correlation coefficient into a statistic that has a sampling distribution that closely approximates the _____ distribution with _____ degrees of freedom.

An investigation of the relationship between years of formal education and IQ that was conducted with a sample size of 100 found a statistically significant correlation of .25.Another investigation of the same relationship had the same r value based on a sample size of 10,but it was not statistically significant.Why might this be?

If a relationship is observed between two variables in a set of sample data,this means that a relationship exists between the variables in the corresponding population.

In terms of regression,the criterion variable is ____ while the predictor variable is _____.

Suppose you were interested in conducting a study examining how ratings of similarity between oneself and another person were related to how attracted one is to the other person.You conduct this study by giving participants a description of a person named "Sarah." Participants are asked to read the description and then rate on a scale from 1 to 10 how similar Sarah is to themselves.You also ask each participant to rate on a scale from 1 to 20 how likeable they think Sarah is. X = rating of similarity to oneself Y = rating of likability of the target ("Sarah") 62 people participate in your study,and you obtain the following data: $\bar{X}=6.00$ SCP = 66 $\bar{Y}=10.00$ SS_X = 40 SS_Y = 136 Calculate the Pearson correlation coefficient (r)for the above data.

Suppose you were interested in conducting a study examining how ratings of similarity between oneself and another person were related to how attracted one is to the other person.You conduct this study by giving participants a description of a person named "Sarah." Participants are asked to read the description and then rate on a scale from 1 to 10 how similar Sarah is to themselves.You also ask each participant to rate on a scale from 1 to 20 how likeable they think Sarah is. X = rating of similarity to oneself Y = rating of likability of the target ("Sarah") 62 people participate in your study,and you obtain the following data: $\bar{X}=6.00$ SCP = 66 $\bar{Y}=10.00$ SS_X = 40 SS_Y = 136 Using your calculations above,if you asked another person who was not in your original experiment to rate the similarity between themselves and "Sarah" on the same scale from 1 to 10,and their rating of similarity = 5,what would you predict their likability rating to be?

A positive correlation between height and weight would indicate that _____.

Imagine you are interested in researching the relationship between job experience and income among early-career working professionals.You take a random sample of 32 professionals from the nearest city,and you ask them to report their annual income and submit a resumé outlining their professional experience.You later calculate their years of experience from their resumés.You compute the following information: How would you state the null hypothesis for this test?

A regression equation can be used to identify the value of Y that is predicted to be paired with an individual's score on X.

Suppose a school psychologist found a correlation between SAT scores of students who graduated from her school and their GPAs at the end of the first year in college.The correlation,r = .82,was based on a sample of 55 students whose SAT scores ranged from 450 to 550.The next year,one for her students made a 625 on the SAT and she wants to predict that students future GPA.Which of the following statements is true?

The Pearson correlation cannot be used to determine the relationship between two variables when _____.

In hypothesis testing for the correlation,if the null hypothesis is rejected and the sample correlation coefficient is positive,this indicates that in the population the correlation coefficient is also ____________________.