Chapter 6: Simple Regression And Correlation Analysis Chapter 6: Simple Regression And Correlation Analysis

Question 1

What is a multivariate dataset

Answer 1

It is a set that consists of observations on two or more variables

Question 2

What is a bivariate data set

Answer 2

It is a set that consists of two variables and the paired observations are denoted by (x1,y1), …, (xn,yn)

Question 3

What is a dependent variable

Answer 3

It is a variable which can be partially explained by the independent variable. Therefore, the dependent variable is dependent on the behaviour of the independent variable

Question 4

What is the assumption of changes in values of y and x

Answer 4

If it is assumed that changes in the value of y are explained by changes in the value of x, x is referred to as the independent variable and y is referred to as the dependent variable.

The independent variable is sometimes also called the predictor variable or the explanatory variable

We occasionally also refer to the independent variable is the response variable

Question 5

What is a scatter plot

Answer 5

A scatter plot is a graphical representation of the values of the independent variable plotted against the dependent variable

The dependent variable is displayed on the vertical axis and the independent Variable on the horizontal axis. Every pair of (x, y) - values is plotted on the graph

Question 6

What is interpolation

Answer 6

Estimates a y-value for a given x-value inside the interval of observed x-values

Question 7

What is extrapolation

Answer 7

Estimates a y-value for given x-values outside the interval of observed x-values

Question 8

What is correlation coefficient

Answer 8

The correlation coefficient is a measure of the strength of the linear relationship between two variables

Question 9

What is the least squares curve

Answer 9

It makes the sum of the squared residuals as small as possible

Question 10

What is a time series

Answer 10

A time series is the set of observations made at different points in time with equal duration between each observation.

Estimating the long-term trend in the timeseries enables the investigator to make predictions into the future

Irregular variation is present in a time series when they are unpredictable movements in the timeseries it as a result a difficult to describe mathematically

Regression methods (such as the method of least-squares) can be used to capture the long-term trend in a time series

Question 11

What is the relationship as x increases and y increases

Answer 11

Positive linear relationship

Question 12

What is the relationship as x increases and y increases but with greater variation

Answer 12

Weaker positive relationship

Question 13

What is the relationship as x increases and y decreases but with greater variation

Answer 13

Weaker negative relationship

Question 14

What is the relationship as x increases and y decreases

Answer 14

Negative relationship

Question 15

What is the relationship as x increases and y increases and decreases

Answer 15

Non-linear relationship

Question 16

What are the properties of the correlation coefficient

Answer 16

-1=<0=<1 The correlation coefficient always lies between -1 and 1

• r > 0 There is a positive linear relationship
• r < 0 There is a negative linear relationship
• r = 1 Perfect positive linear relationship
• r = -1 Perfect negative linear relationship
• r = 0 Non-linear relationship

between x and y

Question 17

What is regression used for?

Answer 17

To forecast y bar for given x-values

Question 18

In the regression equation what does an estimate of a represent and what does an estimate of b represent

Answer 18

a denotes the y intercept
b represents the gradient of the straight line (in other words, for each unit that x increases, the y value will, on average, increase by b units or decrease by b units)

Question 19

What does the y bar symbol indicate

Answer 19

It indicates the straight line fitted through the data points in the scatterplot in such a way that it best describes the overall linear relationship between the variables

NB!! Y bar also represents the mean y value for the x value

Question 20

What are residuals

Answer 20

Residual is the difference between the observed value (y) of the dependent variable and the value given by the estimated regression line
(y-ybar)

Question 21

What is the least squares line

Answer 21

It is obtained by minimising the sum of the squares of the vertical distance between the observed points and the corresponding points on the line

Question 22

What are the properties of the coefficient of determination

Answer 22

0=<Rsquared=<1
- if R = 1 It is a perfect fit of the curve to the observed data
- if R = 0 The curve does not fit the observed data
- For a straight line it is true that r=R

Question 23

What denotes the covariance between x and y

Answer 23

Sxy

Question 24

What are the standard deviations of x and y

Answer 24

Sx and Sy

Question 25

What is the average of residuals

Answer 25

0

Question 26

What is a residual plot

Answer 26

It is a scatterplot of the residuals (on the Y axis) against the ones on the (X axis)

Question 27

What is an outlier

Answer 27

It is an observation outside the general pattern of the other observations

Question 28

Is r dependent or independent of the units used when the observations are measured

Answer 28

Independent