W7 - Regression Flashcards by Holly Tomlinson

What is regression analysis used for?

To predict one variable based upon the score in the other variable.

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What is regression concerned with?

Prediction of 1 variable from a RELATED variable

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In what 3 ways does regression + correlation analysis differ?

In its purpose

How variables are described

The inferential tests

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3 ways in which regression + correlation analysis differ

What is meant by in its purpose

When talking about correlations = talk about relationships, associations + correlations.

Regression analysis = Clearly talking about prediction.

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3 ways in which regression + correlation analysis differ

What is meant by how variables are described

For correlation analysis = makes no difference which variable is on X or Y axis of scatterplot.

Regression analysis = Independent always on X axis, dependent variable always on Y axis.

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3 ways in which regression + correlation analysis differ

What is meant by the inferential tests

Correlation analysis = Primarily interested in the r value.

Regression analysis = Interested in 3 bits of info;

r^2 value (shared variance between 2 variables)
Intercept (a)
Regression coefficient (b)

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What does the regression line on a graph do?

Minimises the vertical deviations of the points from the line

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What does it result in when the vertical distance between the line + points on a scatter plot are minimised?

We are minimising the error of prediction

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For a scatter plot with regression analysis, what is also known as the dependent variable on the y axis?

Predicted variable

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For a scatter plot with regression analysis, what is also known as the independent variable on the x axis?

Predictor variable

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What is the bivariate regression equation?

Algebraic equation expressing the prediction of 1 variable by another

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How is the bivariate regression equation usually written?

Y = a + bX

Also written as:

Y = bX + c

^^ Where C=a

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BIVARIATE REGRESSION EQUATION

What does the Y represent?

Dependent variable

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BIVARIATE REGRESSION EQUATION

What does the a represent?

Constant (Y intercept)

Where the line of best fit would cross through the y axis

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BIVARIATE REGRESSION EQUATION

What does the X represent?

Independent variable

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BIVARIATE REGRESSION EQUATION

What does the b represent?

Regression coefficient (slope)

= Change in y / change in x

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Steps to perform regression analysis

1+2. Consider Null + Alternative hypothesis |(make sure to include WILL or will NOT predict)

Select level of significance
Collect + summarise data
Check assumptions
Run Statistical test
Interpret significance of result

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Steps to perform regression analysis

Give a null hypothesis example for:

Sum of skin fold measures + body fat %

There’s no significant relationship between the variables.

More specifically, the sum of skin folds will NOT predict % body fat.

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Steps to perform regression analysis

Give a alternative hypothesis example for:

Sum of skin fold measures + body fat %

There is a significant relationship between the variables.

Most specifically, the sum of 5 skin folds will predict % body fat.

Steps to perform regression analysis

Select level of significance

Give an example using:

Sum of skin fold measures + body fat %

If our probability level is less than 0.05 (p<0.05), we are 95% confident that explained variability in DXA % body fat by sum of 5 skin folds is greater than one might expect by chance if there was no explained variability in the population.

Steps to perform regression analysis

Assumptions for bivariate regression

Need to ensure data is parametric

What comes under data being parametric?

Normal distribution

Homogeneity of variance

Interval/ratio (continuous)

Independence

Linearity

Residual values are normally distributed

What is the vertical distance between the data points + the line in scatter plots also known as?

Residual distance

Does each point on a scatter plot have a vertical/residual distance?

YES

What does R represent

Simple Pearson correlation coefficient

What does R^2 represent

Coefficient of determination

What must you do when running a statistical test for regression analysis?

Find: - R^2 value - a value - b value

In SPSS what can be found in the analysis of variance box in a table?

Titles: - F - Sig.

Where can the a + b values be found in the SPSS output?

Under the unstandardised coefficients in the coefficients box In column B

What in the coefficients box in SPSS outputs, tells us whether the b-value (slope) is significantly different from 0?

The t statistic + sig. value columns at the end.

List ways in which regression analysis can be used in Exercise + sport sciences

Predicting skill perf from self-efficacy Predicting obesity risk from daily PA levels

Way in which regression analysis can be used in the real world

Pre-London 2012, regression tech were used to predict no. of GB medals

What is the SD of the residual/vertical distances known as?

Standard Error of the estimate (SEE)

How is a prediction interval created using SEE?

z-score (i.e 1.96) x SEE

What is a regression equation used for?

To estimate the value of the DV based on the value of the IV

In bivariate regression, if the slope of the regression line was 2.1, this would mean....

That for every increase of 1 on the X axis there is an increase of 2.1 on the Y axis

What does variance of a single variable represent?

The avg amount that the data may vary from the mean

How do you calculate the exact similarity between the patterns of differences of the 2 variables in the single-variable case?

Square the deviations - to eliminate the problem of +ive + -ive deviations cancelling each other out.

How do you calculate the exact similarity between the patterns of differences of the 2 variables in the 2-variable case?

Multiply the deviation for 1 variable by the corresponding deviation for the 2nd variable. To get the cross-product deviations.

What is covariance?

The avg sum of combined deviations

What does a +ive covariance indicate?

That as 1 variable deviates from the mean, the other variable deviates in the same direction.

What does a -ive covariance indicate?

That as 1 variable deviates from the mean, the other deviates from the mean in the opposite direction.

Between what values must the correlation coefficient lie between?

-1 + 1

What is the spearman's correlation coefficient?

Non-parametric statistic Useful to minimise the effects of extreme scores or the effects of violations of the assumptions.

In regression analysis, what assumptions do we need to check to see if the data is parametric?

Normality Linearity Homogeneity of variance Independence Interval/ratio data Normally distributed residuals

Which assumptions can be examined using a scatterplot graph?

Linear relationship Homogeneity of variance