Quantitative Methods - Correlation And Bivariate Linear Regression

Question 1

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

Answer 1

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

Question 2

What is Regression?

Answer 2

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

Question 3

What is Correlation?

Answer 3

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

Question 4

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

Answer 4

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.

Question 5

What are the regression coefficients or parameters?

Answer 5

A and b or their equivalents

Question 6

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

Answer 6

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

Question 7

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

Answer 7

Y = a+bx

Question 8

What is bivariate or simple linear regression?

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

Interpolation or extrapolation from given expectations regarding the independent variable

Question 11

What is the output of regression analysis?

Answer 11

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

Question 12

What does the coefficient b mean in regression analysis?

Answer 12

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.

Question 13

What does the coefficient A mean in regression analysis?

Answer 13

This gives the value of Y when X is zero

Question 14

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

Answer 14

The Least Squares Method.

Question 15

What is the least squares method?

Answer 15

The method of estimating the parameters a and b

Question 16

What is the idea behind the Least Squares Method?

Answer 16

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!

Question 17

What is minimising the sum of the squared errors ?

Answer 17

The vertical distances of the points away from the line are added and then squared to ensure we only consider the absolute value of any distance and not e direction as all the numbers are positive. It also ensure large distances from the line are avoided, since the squaring process exaggerates the larger distances.

Question 18

How will the regression equation be often expressed and why is it expressed so?

Answer 18

Y = a + bx + e

The e is an error or disturbance term. If the regression line represents the best linear unbiased estimate of the relationship between x and y, the error term will have a random variable with a mean of zero. It reflects that we cannot guarantee the value of y will be as predicted. On a random basis, the actual value will lie both above and below the predicted value.

Question 19

What is the purpose of the correlation measure?

Answer 19

To measure the strength of the relationship between two variables. In the context of regression analysis with only one independent variable, the correlation coefficient will give an indication of how accurately the regression line matches the observed values

Question 20

What is the correlation coefficient?

Answer 20

A relative measure indicating how two variables move with respect to each other. It is also called the Pearsons correlation coefficient. When a correlation coefficient is calculated by reference to a sample of data, it is referred to by the symbol r. When calculated by reference to a population, it is referred to as P (pronounced rho)

It measures the direction and degree of linear association between the two variables. It will have a value between + and - 1 and the meaning of the correlation coefficient can be best understood by considering extremes

Question 21

What is perfectly positive correlation?

Answer 21

A correlation coefficient of + 1. Two variables will move up and down together and in proportion.

Question 22

What is non-perfect positive correlation?

Answer 22

A correlation coefficient between 0 and 1. The line will still go up just the points won’t all be on it

Question 23

What is perfect negative correlation?

Answer 23

A correlation coefficient of -1

The two variables will move up and down in exact opposition and in proportion.

Question 24

What is uncorrelated?

Answer 24

Correlation coefficient of 0

Two variables move independently of each other

Question 25

Generally what is viewed as a moderate correlation?

Answer 25

0.5

Question 26

What is viewed as weak correlation?

Answer 26

Less than 0.5

Question 27

What is viewed as strong correlation?

Answer 27

Above 0.5

Question 28

What are the two relevant factors in a correlation coefficient?

Answer 28

The sign (+ or -) and the value

Question 29

What are the effects of the two relevant factors in the correlation coefficient?

Answer 29

Positive correlation implies that variables move up and down together, negative correlation means that they move in opposition. The value of the figure, ignoring the sign gives an indication of the strength of the relationship, the closer to one, the stronger the relationship

Question 30

What is the link between the correlation coefficient and the b coefficient in the regression equation?

Answer 30

If the correlation coefficient is positive/negative then coefficient b will also be positive/negative. If there is no correlation B will be zero

Question 31

What is significant about the B coefficient compared to the correlation coefficient?

Answer 31

The B coefficient gives more info than the correlation coefficient since it not only shows the direction of the relationship, it also shows by how much the dependent variable will change. However us of the B coefficient involves the limiting assumption that the dependent variable is a function of the independent variable. It is not necessary to designate a dependent and independent variable when calculating the correlation coefficient.

Question 32

What is a spurious relationship?

Answer 32

When two things may appear related but actually aren't such as wasp stings and ice cream production.

Question 33

What is important about causality?

Answer 33

A regression relationship and high correlation in themselves do not love causality.

Question 34

What is data mining?

Answer 34

The process of economists sorting through data looking for info that may be relevant, but may actually be spurious relationship.

Question 35

What can the regression line be used for?

Answer 35

To estimate a value for y given a value for x

Question 36

What is interpolation?

Answer 36

Where we try to estimate profits that will arise from sales within the already observed range

Question 37

What is extrapolation?

Answer 37

Where we try to predict profits that will arise beyond (either above or below) the observed range of sales

Question 38

What is the validity of interpolation and extrapolation?

Answer 38

Estimating profits levels arising from sales within an item range, should provide reasonable results since there is data to support our conclusions Estimating profits arising outside the range could be dangerous since we have no data to support the results we will be estimating. It is quite possible that a relationship that appears linear over a short range of values turns out to be non-linear when we move beyond those values, making any extrapolated results worthless or even dangerous. However this data can be used to establish an expected value or forecast, and use the variability of the data to try to establish confidence limits within which we can be sure, with a given degree of confidence, that the observed value will lie.

Question 39

What are some issues with regression and correlation analysis?

Answer 39

They work for linear relationships, however many business and economic relationships do not follow linear trends and have much more complicated relationships.

Question 40

What is multiple regression?

Answer 40

Where the y axis may be dependent on more than one independent variable.

Question 41

What do regression and correlation analysis do?

Answer 41

Enabled us to quantify relationships. The purpose of this enables us to estimate a specific point on one access if we know the value of the corresponding point on the other access