# Quantitative Methods - Correlation And Bivariate Linear Regression Flashcards

What is more method to show the relationship, which isn’t hugely precise?

Place a ruler and draw a line, this works reasonably well if all the plotted points are roughly in a straight line

What is Regression?

The equation of the line of best fit mathematically, giving a much more accurate result that the visibly drawn line.

What is Correlation?

An indication of the accuracy or strength of the relationship, I.e. Whether this line is a good or poor explanation of the relationship between the two variables

What is the equation of a strait line on a graph?

Y = a + bx

A= the height at which the line cuts the y axis B= the slope, ie the change in the value of y unit per unit change in the value of x

However there are other notations for writing this.

What are the regression coefficients or parameters?

A and b or their equivalents

Typically, when dealing with a population what notation for a straight line do we use?

y = a+bx (both the b and a are big and weird)

Typically when dealing with a sample how will the notation for a straight line appear?

Y = a+bx

What is bivariate or simple linear regression?

Where a relationship exists between two variables, one of which will drive/determine the value of the other

In terms of regression, what does the independent variable allow?

If we can identify a value for the independent variable, we can use this to predict the value for the dependent variable

With regards regression, how will we predict the value of the dependent variable?

Interpolation or extrapolation from given expectations regarding the independent variable

What is the output of regression analysis?

The two coefficients a and b hitch determine the relationship between the two variables

What does the coefficient b mean in regression analysis?

The gradient of line. If this is 2 it means an increase on the x axis of 5 will see the y axis increase by 10.

If B is positive the line will be upward sloping suggesting y is directly proportional to the value of x

If B is negative the line will be downward sloping suggesting y is inversely proportional to the value of x.

What does the coefficient A mean in regression analysis?

This gives the value of Y when X is zero

The method for estimating the parameters A and B is referred to as what?

The Least Squares Method.

What is the least squares method?

The method of estimating the parameters a and b

What is the idea behind the Least Squares Method?

In calculating the regression line we want the line of best fit. Is implies that all the actual values on the graph on the graph are reasonably close to the line. It is usually not possible to make all the values very close at the same time, since we are making a straight line meaning some values will be further from the line than others!