psy 202 final

Pearson correlation coefficient (Pearson product-moment correlation coefficient)

A correlation statistic used to measure linear relationship between variables that have interval- or ratio-level measurements.

Covariance

A measure of the relationship between the two variables that is based on the distances of the values of the variables from their means.

Predictor variable:

A measured variable used to estimate the strength and direction of an outcome, or dependent, variable in a correlational or regression analysis. Sometimes referred to as an independent variable.

Bivariate linear regression

A procedure in which the linear relationship between a single interval- or ratio-level predictor variable is used to predict the value of an interval- or ratio-level outcome variable.

Method of least squares

A regression procedure that yields an equation that results in the lowest possible sum of squared residuals (SSresidual) when x and y have a Pearson correlation coefficient equal to r.

Spurious correlation

A relationship between two variables that is not due to a causal relationship.

Negative correlation

A relationship in which two variables change in opposite directions, with one variable increasing and the other decreasing. An inverse relationship.

Positive correlation

A relationship in which two variables change in the same direction, either both increasing or both decreasing.

Correlational analysis

A statistical test used to analyze relationships, or the extent to which changes in one variable are related to changes in another variable.

F-statistic

A test statistic in a regression analysis that represents the ratio of improvement in predictions by the model to the level of error in the model. Also known as the F-ratio.

Confound

A variable that changes with, and is empirically inseparable from, the independent variable of interest, making it impossible to differentiate the x variable's effects in isolation.

What is missing from the following APA style summary of the results of a bivariate linear regression? F(1, 8), p = < .001, r2 = .99

F-statistic

Dr. Robles has conducted a regression analysis, but to test their assumptions, the outcome variable is plotted on the x-axis against the outcome residuals on the y-axis. Upon viewing the resulting scatterplot, they observe that the plot is linear but but has a steep slope. What statistical assumption has most likely been violated?

Independence of errors

Intercept

The point at which either axis of a graph is intersected by a line plotted on the graph. For example, it is the value of y when x = 0 in an equation of the form y = bx + a, or the value of x where a regression line crosses the y-axis.

Coefficient of determination

The proportion of variance in y that can be explained by x. Also known as r2.

Across the years 1990 to 2006, there was a correlation of r = −.80 between annual new passenger car sales and the annual average cost of red delicious apples, such that as new passenger car sales decreased, the cost of red delicious apples increased (Vigen, n.d.a). What else should be reported for this correlational analysis?

The result of hypothesis testing, including p value

Correlation coefficient

The sample statistic in a correlational analysis that quantifies the linear relationship between two variables and ranges from +1 to −1.

Slope

The steepness or slant of a line on a graph, measured as the change of value on the y-axis associated with a change of one unit of value on the x-axis. In a regression equation, slope is represented by the notation b.

If there is a confounding present in the correlational relationship between homework assignments completed and exam scores, then

at least one additional variable is involved in the relationship.

The Pearson correlation coefficient provides information about the _____ of a relationship.

direction and strength

For an observation in a data set with two variables, x and y, the larger the absolute value of the product zxzy, the

farther that point will be from the center of the scatterplot of x and y.

Effect size is used to determine

if an effect is meaningful, or important.

Graphing a correlation can tell you

if the relationship is at least approximately linear

The method of least squares assures us that the regression equation

is the best fitting line and minimizes SSerror.

If r = .96, then the relationship between the variables of interest is

nearly as strong as mathematically possible.

A r2 value close to 1 indicates

that much of the variation in y can be explained by x.

In the regression equation ŷ = bx + a, the a term represents

the point at which the regression line crosses the y axis.

Which value of r represents the strongest relationship between two variables?

−.81

The smallest possible value for r2 is

.00

If r = −.10, select the correct value for the coefficient of determination (in decimal form, not as a percentage).

.01

A bivariate linear regression was conducted with a sample size of 30 where height was regressed on weight. What is the degrees of freedom value of the numerator of the F-ratio for this analysis?

1

2. Jan and colleagues (2017) analyzed the regression of self esteem (y) on time spent on Facebook (x) and found r2 = .871. Select the appropriate interpretation of this value.

87.1% of the variance in self-esteem can be explained by time on Facebook.

Drs. Ngayabaseka and Uwimana are collaborators on a study investigating grazing rights of indigious tribes of Burundi and Rwanda. In the course of their study, they conducted a bivariate regression analysis with a sample size of 501 resulting in a regression mean square of 5.500 and a residual mean square of 1.445. What is the F-statistic for this regression and is it statistically significant?

3.81, no

Outcome variable

An effect that one wants to predict or explain in correlational or regression research. Also referred to as a dependent variable.

Outlier

An observation with an extreme value on one or more variables that suggests there may be something unusual about that observation, perhaps that it represents a population different from the remaining observations.

Which scenario is appropriate for a bivariate linear regression analysis?

Analyzing if total years of school is a significant predictor of annual income.

Regression analysis

Any of several statistical techniques that are used to describe, explain, or predict (or all three) the variance of an outcome or dependent variable using scores on one or more predictor or independent variables.

Zero correlation

Changes in the values of one variable are not related to changes in the value of the other variable.

Matthews (2000) identified the bivariate regression equation ŷ = .03x + 225.03, with the predictor variable number of stork breeding pairs and the outcome variable human birth rate (1000s/year). Which of the following is the appropriate interpretation of the slope?

For every 1 stork breeding pair, the human birth rate (1000s/year) increases by .03.

Which of the following includes all the statistics that should be reported for a correlational analysis?

M, SD, n, r, p

Imagine researchers find a positive correlation between dark chocolate consumption and weight loss. Can we conclude that eating chocolate causes weight loss?

No, because it is possible that another variable could be causing increased chocolate consumption and weight loss.

Researchers assigned each participant to use one of three memory techniques and then measured mean memory scores for each group. Is a correlational analysis appropriate for this scenario?

No, because one of the variables is categorical.

Each deviation score for a residual sum of squares is calculated as the difference between what two values?

Outcome value and predicted mean (y - ŷ)

Residual

The difference between the observed value of the outcome variable y and its predicted value ŷ for a given value of the predictor variable x in a regression procedure. Also known as error.

Regression model

The mathematical equation for the relationship between an outcome (dependent) variable and one or more predictor (independent) variables that results from conducting a regression analysis. For a linear bivariate regression, this is ŷ = bx + a.

In everyday language, the term correlation means about the same thing as relationship or association. In statistics, the more technical meaning of the word refers to

a measure of the direction and strength of a relationship between two variables.

Dr. Orion finds a negative correlation between hours of sleep and proportion of pessimistic responses. The direction of the correlation indicates that

as hours of sleep increase, the proportion of pessimistic responses decrease.