midterm review

Question 1

Define Simple Linear Regression

Answer 1

A dependent variable (ex. Y) is predicted from one independent variable (ex. X) based on a linear relationship

Question 2

Define Regression

Answer 2

The relation/dependency of & between 2 variables

Question 3

SLR equation

Answer 3

y = a + βx

Question 4

Define Residuals

Answer 4

The differences between the real data & the line

Question 5

Goal with SSR

Answer 5

To find THE line that minimizes the SSR

Question 6

Define Stock “Beta”

Answer 6

Beta is a risk measure of stock investment, calculated as the coefficient of the market return

Question 7

When |β| > 1…

Answer 7

Stock is riskier & its returns have greater volatility (change unpredictable)

Question 8

When |β| < 1…

Answer 8

Stock is less risky & its returns swing less than market returns

Question 9

Monthly return formula

Answer 9

Monthly return = (Current month-end price - Last month-end price)/Last month-end price

Question 10

Basic set-up for lm() function

Answer 10

regression_analysis_result_name <- lm(Y ~ X, data)

Question 11

How to calculate SD manually

Answer 11

1. (y-µ)^2
2. square all results from step 1 + divide by count

Question 12

How to manually calculate Q1 & Q3

Answer 12

1. split dataset into 2 halves
2. find the median of each half

Question 13

How to find IQR

Answer 13

Q3-Q1

Question 14

How to calculate Lower & Upper Whisker

Answer 14

LW = Q1 - 1.5IQR
UW = Q3 + 1.5IQR

Question 15

How to calculate Extreme Lower & Upper Whisker

Answer 15

eLW = Q1 - 3IQR
eUW = Q3 + 3IQR

Question 16

Difference in using summarize() & mutate()

Answer 16

must use <- when mutating to save the new variable into a dataset

Question 17

When do you $?

Answer 17

When you are referring to a specific dataset for a variable

Question 18

Define Probability Density Curve

Answer 18

Density curve visualizes the probability distribution → how probabilities are distributed over the values of a random variable

Question 19

Advantages of Probability Density Curve

Answer 19

• A more refined representation of data
• Facilitate the probability calculation (even if data is absent)

Question 20

Describe Skewed distribution

Answer 20

Mean > Median → Right-skewed
Mean < Median → Left-skewed

Question 21

Density Curve Properties

Answer 21

• A density curve must lie on or above the horizontal axis
• The area under the density curve always equal to 1 or 100%
  > Cannot be on y-axis or be below x-axis

Question 22

Relationship between Probability Density & Probability

Answer 22

Probability Density ≠ Probability
- For a continuous variable, discussing its probability of being a specific value is not meaningful because it always equals to zero

Question 23

Meaning of PD & Probability

Answer 23

Probability = area
Likelihood = height = density = straight line

Question 24

Representation of Normal Distribution

Answer 24

If a random variable follows a normal distribution, it is presented as:
X ~ N (µ, σ)
Mean → center of the curve
Stdev → wideness of the curve

Question 25

How to find z-score in standard normal table

Answer 25

1. Find the row that matches the (signed) first 2 digits of the z-score
2. Find the column that matches the (signed) third digit of the z-score
3. Find the probability value in the cell where the row & column meet

Question 26

Define Standardization

Answer 26

Transforming a general normal distribution (ex. N ~ X (µ, σ)) to a standard normal distribution (ex. Z ~ N (0, 1))

Question 27

If a dataset follows a (general) standard normal distribution, then

Answer 27

68% of the data lies within one standard deviation of the mean
95% of the data lies within two standard deviations of the mean
99.7% of the data lies within three standard deviations of the mean

Question 28

FInd Pr (-1 < Z < 1) using R code

Answer 28

pnorm(1, mean=0, sd=1) - pnorm(-1, mean=0, sd=1)

Question 29

Checks for Normality

Answer 29

1. Histogram & Density Curve → bell-shaped & symmetric around the mean
2. Empirical Rule intervals → 68%, 95%, 99.7%
3. IQR-to-SD ratio = 1.3
4. Quantile-Quantile (Q-Q) Normality Plot

Question 30

2 questions related to Population vs Sample

Answer 30

1. Can we make accurate inferences about the population based on a sample of data? (Today’s class)
2. How confident can we be in these inferences? (After the reading week)

Question 31

Define Parameter

Answer 31

A numerical value that describes a specific characteristic of an entire population

Question 32

Define Sample Statistic

Answer 32

A sample of data

Question 33

What is the meaning behind Statistical Inferences

Answer 33

Want to make informed inferences about the unknown population parameter based on the sample statistics

Question 34

Define normal distribution

Answer 34

A perfectly normal distribution would appear as a symmetric, bell-shaped curve centered around the mean but not smooth

Question 35

What is the SD of the sample means

Answer 35

Standard error
- ~ 10 times smaller than the population SD

Question 36

Define Central Limit Theorem

Answer 36

The variance between sample mean & actual mean decreases the more samples that are generated
- As the # of samples increases, the distribution starts to indicate a normal distribution with a smooth bell-shaped curve, more closely adhering to the normal distribution’s characteristics