correlation

Question 1

bivariate data

Answer 1

pairs of values as variables

Question 2

independent variable

Answer 2

x axis ( explanatory variable)

Question 3

dependent

Answer 3

y axis (response variable )

Question 4

types of corelation

Answer 4

strong negative, weak negative strogn positive, weak positve

Question 5

casual relationship

Answer 5

if one variable causes a change in the other !

Question 6

comment on the claim that hotter coutnries have less rainfall

Answer 6

the graph does not support the statement that hotter coutnries have less rainfall !

Question 7

“describe and interpret the corellation between 2 variables “

Answer 7

there is a positive/negative corelation since as ……. increases/decrerases, ??????? increases/decreases

Question 8

there is a weak negative corelation between internet speed and house value. danyal concludes this ; suggest why he may be wrong

Answer 8

there may be 3rd variable that influences house value and internet connection - eg distance from built up areas

Question 9

outlier formula

Answer 9

upper: q3 + 1.5(IQR) Lower: q1` - 1.5 (IQR)

Question 10

give a reason why you might exclude an anomaly give a reason for including an anomally ?

Answer 10

exclude: anomally is an outlier and not representative
include: “anomally” part of distribution data so include it

Question 11

what kind of corellation is this ?

and what does it show

Answer 11

weak negative ( overall downward trend )

a casual relationship between two variables

Question 13

type of line of best fit

Answer 13

least squares regression line

regression line that minimises sum of squares of distrances of each data point

D=point on graph

minimses value of… D1 ^2 + D2^2 + D3^2etc.. .

(x,y)

Question 14

formula for regression line

Answer 14

y= a +bx

order of variabels = importnat

regression line of y on x is different from x on y

coefficent (B) = changei n y for each unit of change in x, example: if b is negative…then data negatively correlated

vice versa

Question 15

w= windspeed ( knots)

g= gust ( knots)

give an interpretation of the value of the gradient of this regression line?

Answer 15

just say what the gradient does…

if the valeu of windspeed is 10 knots (Exmaple ) , the daily maximum ust increases by 18 knots

Question 16

justify the use of a linear regression line ?

Answer 16

because corelation suggests a linear relationship!

Question 17

when should you use lienar regression line ?

Answer 17

values of dependent variable that ware within a range of given data ( interpolation )

Question 18

value is inside the range of data so is linear regrression used

Answer 18

said value is within the range of data so linear regression is more likely to be accurate

if outside the data ( extrapoaltion), linear regressio nlessl ikely to be accurate

Question 19

regression equation y= 2 + 6x

man wants to estimate x from y ( x is independent variable.. y is dependent variable !)

suggest why this is bad

Answer 19

independent variable is x , you shoudl onyl make predicitons for dependent variable! so you sohuld not use this model to predict a value of x for a given value of y !

isntead, you need to use regression line of x on y

Question 20

line of regression common question

comment of the reliability of said valeus x and y ( y is outside of the range of values )

Answer 20

x is reliable as its within the range of data

y is not reliable as it is outside the range of data

Question 21

Answer 21

There are two key problems with Helen’s statement: First, 10 coats of paint is very far outside our range of given data, and we cannot assume that this linear relationship continues as we extrapolate, so using the regression line is not necessarily valid. Second, even if we accept the extrapolation as valid, a gradient of 1.45 means that, for every extra coat of paint, the protection will increase by 1.45 years. Therefore, if 10 coats of paint are applied, the protection will be 14.5 years longer than if no paint were applied. Helen has, however, forgotten to include the constant 2.93 years, which is the weather resistance if no paint were applied. After 10 coats of paint the protection will last approximately 2.93 + 14.5 = 17.43 years.

comment on how data is outside of range of valeus thus extrapolation may not be correct for this regression equation

comment on the fact that the constant has not been included !

Question 22

note

Answer 22

if negative weak corelation present, then the coefficient of gradient on regression line should be negative

Question 23

the equation for the line of regression for houses….

y= 900 + 5x

x= number of bedrooms

person says that if there is no bedrooms, the price of the house will be 900

why is this unreasonable ?

Answer 23

This is not a reasonable statement as there are unlikely to be any houses with no bedrooms, so she is extrapolating outside of the range of data, where the linear relationship is unlikely to continue.

Question 24

regression equation should be used to give a value for.,,

v= h + 100x

Answer 24

v given h

(this is an example !)