Statistics in R: Class test 1

Question 1

Describe the two different types of categorical data

Answer 1

Nominal data - Data items placed into discrete classes. There is no inherent order between categories (Gender, Blood Group)
Ordinal data - numbers (or letters) acting as labels only, data are
placed in an order based on their value. Various categories can be logically arranged in a meaningful order (Ranks, Grades)

Question 2

Describe the difference between interval and ratio data

Answer 2

For interval data doubling is not meaningful and there is no true zero (Temperature). For ratio data these two factors are meaningful, such as distance

Question 3

Describe the difference between continuous and discrete data

Answer 3

Continuous data has an infinite number of values such as weight where a value of 1.5kg is meaningful.
Discrete data is has a set number of values, for example 1.5 fingers is not meaningful

Question 4

What indicates that a dataset is normally distributed?

Answer 4

68% of data is + or - 1 standard deviation away from the centre mean

Question 5

Define the mean, median and mode

Answer 5

Mean - average of all values
Mode - the value that occurs most frequently
Median - the middle value

Question 6

What are the null hypothesis and the alternative hypothesis?

Answer 6

Null hypothesis - there is no significant difference, correlation or relationship
Alternative hypothesis - there is a significant relationship correlation or difference

Question 7

What is a Type I and Type II error?

Answer 7

A Type I error is a false rejection of the null hypothesis
A Type II error is the non-rejection of a false null hypothesis

Question 8

What is the p-value?

Answer 8

The p-value is a measure of whether the results of your test could have occurred by chance. If the p-value is <=0.05 then the results are significant and the null hypothesis can be rejected

Question 9

What does Pearson’s correlation coefficient(r) tell us?

Answer 9

The strength and direction of a linear, normally distributed, numerical relationship between two variables between -1 and +1 with values close to +1 and -1 indicating correlation and close to 0 indicating no relationship

Question 10

Why is linear regression used?

Answer 10

To determine the line of best fit in a dataset that is linear, normally distributed and numerical and make predictions based of this

Question 11

What are residuals?

Answer 11

Residuals are the difference between observed values and the predicted values from the line of best fit

Question 12

What does the Coefficient of Determination(r^2) tell us and how is it found?

Answer 12

The Coefficient of Determination tells us how much of the variance in the response variable is caused by the explanatory variable and is found by squaring Pearson’s(r)

Question 13

What does the Adjusted r^2 value tell us?

Answer 13

Adjusted r^2 tells us the amount of variance explained by the model but adjusts for the number of terms in the model

Question 14

What is the formula for multiple linear regressions analysis?

Answer 14

y = m1ev1 + m2ev2 + … + c

Question 15

How would you visualise the relationships between the RV and EVs in a multiple linear regression analysis?

Answer 15

Using a pairs plot, you are able to visualise all single linear regression models between the variables

Question 16

What are the steps to determining the minimum sufficient model?

Answer 16

1. Create your model that includes all explanatory variables
2. Check all explanatory variables are significant (p>0.05)
3. Remove the least significant term from the model
4. Run the model again until all explanatory variables are significant

Question 17

What are the key assumptions when undertaking linear regression?

Answer 17

1. Constant variance of residuals
2. Normal distribution of residuals

Question 18

What indicates on the residuals vs fitted y-values that residuals have constant variance?

Answer 18

The “sky at night” pattern with no obvious structure indicates constant variance

Question 19

What indicates on a QQ plot that residuals are normally distributed?

Answer 19

All points are lying on a 45 degree slope or close to it

Question 20

When is it appropriate to use Pearson’s corelation coefficient and linear regression?

Answer 20

When all values are numerical, normally distributed and linear

Question 21

What is a contingency table and what does it show?

Answer 21

A contingency table is a table in a matrix format that display the frequency distribution of variables

Question 22

When can the Kendall and Spearman corelation coefficients be used?

Answer 22

When data is interval or ordinal, non-normally distributed and relationship is non-linear