chapter 4 - Correlation and Regression

Question 1

what is the purpose of correlation and regression

Answer 1

to understand the relationship between a dependent variable and one or more independent variables

Question 2

what does correlation and regression help in [ got 3]

Answer 2

• identifying trends and patterns in data
• making predictions about future values based on past data
• quantifying the strengths and directions of relationships between variables

Question 3

what does the dependent variable [ the response variable] represent

Answer 3

the output or outcome whose variation is being studied

Question 4

what does the independent variable [ the explanatory variable] represent

Answer 4

it represents the inputs or causes i.e. potential reasons for variation

Question 5

what is the purpose of a scatter diagram

Answer 5

to visually represent the relationship between two variables

Question 6

what do scatter diagrams do

Answer 6

they help identify patterns, trends, and the potential strength of correlation between them

Question 7

What is the X-axis also known as

Answer 7

the horizontal axis, the independent variable or explanatory variable

Question 8

what is the Y-axis also known as

Answer 8

the vertical axis, the dependent variable or response variable

Question 9

what does the dependent variable represent

Answer 9

the output or outcome whose variation is being studied

Question 10

what does the independent variable represent

Answer 10

the inputs or causes

Question 11

what is the regression line also known as

Answer 11

best fit line

Question 12

what is the sum of squared errors

Answer 12

the total of all squared differences between actual and predicted results

Question 13

what does the best fit line need to do

Answer 13

the best fit line is the one that makes the SSE as small as possible, ensuring a good representation of the data

Question 14

how does the gradient affect the slope

Answer 14

• when the gradient is positive, the line is sloped upwards
• when the gradient is negative, the line is sloped downwards

Question 15

when asked to predict a future value, which variable do you choose

Answer 15

the y data

Question 16

when asked to find the regression of A data on B data, which is the x and which is the y variable

Answer 16

the a data must be the y variable and the b data must be the x variable

Question 17

how to know if a line is accurate [3 points]

Answer 17

• does the scatter diagram indicate that a straight line is appropriate
• are the plotted points close to the line
• are the forecast for a value of x within or outside the range of values X is given

Question 18

what is interpolation

Answer 18

if the x is within the range, the accuracy is likely to be better

Question 19

what is extrapolation

Answer 19

if the x is outside the range, the accuracy of the estimate is likely to be low

Question 20

what does the product moment correlation of coefficients measure

Answer 20

the strength and direction of a linear relationship between two variables and indicates how well the regression line fits the data

Question 21

what does the correlation coefficient measure

Answer 21

how good a fit the regression line to the data

Question 22

for product moment correlation coefficient, what does it mean if r is numerically greater than 1

Answer 22

you must have made a arithmetic/ numerical error

Question 23

what does it mean in product moment correlation coefficient when r > 0 and r is nearer to 1

Answer 23

there is a strong positive correlation between x and y

Question 24

what does it mean in product moment correlation coefficient when r > 0 and is near to 0

Answer 24

there is a weak positive correlation between x and y

Question 25

what does it mean in product moment correlation coefficient when r < 0 and is near to -1

Answer 25

there is a strong negative correlation between x and y

Question 26

what does it mean in product moment correlation coefficient when r < 0 and r is near to 0

Answer 26

there is a weak negative correlation between x and y

Question 27

what does noise mean in data

Answer 27

noise refers to random variations or unexplained fluctuations in data that obscure true relationship between variables

Question 28

what are some sources of noise [ 4]

Answer 28

- measurement errors - external factors [ economic conditions, weather] - sampling variability - human error in data collection

Question 29

what does the amount of noise represent

Answer 29

the strength of a linear relationship

Question 30

how can noise be determined

Answer 30

the calculation of mean square errors

Question 31

what does correlation indicate

Answer 31

how strongly two variables are related to each other

Question 32

what does correlation not imply

Answer 32

that one variable causes the other to change

Question 33

what does the coefficient of deter,onation show

Answer 33

how much of the variation of y can be explained by the explanatory variable

Question 34

how to find the coefficient of determination using product moment correlation coefficient

Answer 34

js take r square/ r2

Question 35

what is the simplest procedure when data is given in order of merit

Answer 35

a rank correlation coefficient

Question 36

what does the product moment correlation coefficient assume

Answer 36

that the distribution of x and y are known

Question 37

when the distribution of x and y are not known, which method should be used

Answer 37

the rank correlation coefficient should be used

Question 38

why does the value of spearman's rank correlation coefficient differ from the value of the product moment correlation coefficient?

Answer 38

the product moment correlation coefficient use the original data, whereas Spearman's rank correlation only used the ordered data, thus losing some accuracy in the accuracy of the information