midterm 2

Question 1

what are the formulas for regression?

Answer 1

• y = mx + b (slope intercept form of a line)
• m = nΣxy - ΣxΣy / nΣx^2 - (Σx^2) (slope of line of best fit)
• b = ȳ - mx̄ (y-intercept of the line of best fit)

Question 2

what is the formula for spearman’s coefficient?

Answer 2

s = 1 - 6ΣD^2 / n(n^2 - 1)

Question 3

what is the formula for exponential smoothing?

Answer 3

F(t+1) = αy(t) + (1 - α)F(t)

Question 4

what is the formula to calculate simple averages

Answer 4

simple average = Sum of all data points / Number of data points

Question 5

what is the formula to calculate moving averages?

Answer 5

moving average (eg. 3 months) = Sum of data points in last 3 periods / 3

Question 6

how do you calculate sum of squared errors (SSE)?

Answer 6

1. find the errors - for each data point, subtract the forecasted/line of best fit value from the observed value: Error(i) = Actual(i) - Predicted(i)
2. square each error: Error(i)^2
3. Sum the squared errors: SSE = Σ(Error(i))^2

Question 7

what is the formula for the correlation coefficient?

Answer 7

r = nΣ(xy) - ΣxΣy / √ (nΣx^2 - (Σx)^2) (nΣy^2 - (Σy)^2)

Question 8

what are variables?

Answer 8

numbers that can change

Question 9

what does y represent?

Answer 9

the value on the vertical axis (y-axis)

Question 10

what does x represent?

Answer 10

the value on the horizontal axis (x-axis)

Question 11

what does m represent?

Answer 11

the slope of the line of best fit (how much y changes when x increases by 1 unit)

Question 12

what does b represent?

Answer 12

the y-intercept of the line (where the line crosses the y-axis when x = 0)

Question 13

what does n represent?

Answer 13

the number of data points

Question 14

what does Σx mean?

Answer 14

the sum of all the x variables

Question 15

what does Σy mean?

Answer 15

the sum of all the y variables

Question 16

what does Σxy mean?

Answer 16

the sum of the product of each pair of x and y values (multiply each x-value by its corresponding y-value, then add up all those results)

Question 17

what does Σx^2 mean?

Answer 17

the sum of all the squares of x-values (for each x-value, square it, then add up all those values)

Question 18

what does Σy^2 mean?

Answer 18

the sum of all squares of y-values (for each y-value, square it, then add up all those values)

Question 19

what does (Σx)^2 mean?

Answer 19

the square sum of x-values (add up all the x-values, then square the total)

Question 20

what does (Σy)^2 mean?

Answer 20

the square sum of y-values (add up all the y-values, then square the total)

Question 21

what does ȳ represent?

Answer 21

the average of all y-values

Question 22

what does x̄ represent?

Answer 22

the average of all x-values

Question 23

what does S represent?

Answer 23

spearmans coefficient (always between -1 and 1)

Question 24

what does it mean if S = 1?

Answer 24

there’s a positive relationship between the two sets of ranks (meaning as one variable’s rank goes up, the other does as well)

Question 25

what does it mean of S = -1?

Answer 25

there's a perfect negative relationship between the two ranks (as one rank goes up, the other goes down)

Question 26

what does it mean of S = 0?

Answer 26

there's no relationship between the ranks

Question 27

what does D represent?

Answer 27

the difference between the ranks of each pair of items

Question 28

what does ΣD^2 mean?

Answer 28

the sum of all squared rank differences (for each item, find the rank difference, square it, and then add up all those squared values)

Question 29

what does n(n^2 - 1) mean?

Answer 29

it is a normalizing factor that ensures S falls between -1 and 1

Question 30

what does it mean if S is close to 1?

Answer 30

the two ranks are very similar (a strong positive correlation)

Question 31

what does it mean if S is close to -1?

Answer 31

the ranks are inversely related (as one rank goes up, the other goes down)

Question 32

what does it mean if S is near 0?

Answer 32

there's little to no rank correlation

Question 33

what does F(t+1) represent?

Answer 33

the forecasted value for the next period (or future data point)

Question 34

what does α represent?

Answer 34

the smoothing constant (a value between 0 and 1 that controls how much weight is given to the most recent data points)

Question 35

what does a higher α (closer to 1) mean?

Answer 35

more weight is given to the recent data point, making the forecast more volatile

Question 36

what does a lower α (closer to 0) mean?

Answer 36

makes the forecast rely more on the previous forecasted value, making the forecast more stable

Question 37

what does Y(t) represent?

Answer 37

the actual value observed for the current period (the latest data you have)

Question 38

what does F(t) represent?

Answer 38

the forecasted value from the previous period, which provides a baseline (or trend) from past predictions

Question 39

what is the line of best fit?

Answer 39

a straight line that best represents the data on a scatter plot, it is used to show the relationship between two variables

Question 40

what is the formula to calculate line of best fit?

Answer 40

y = mx + b

Question 41

what is exponential smoothing?

Answer 41

applies a smoothing constant (α) to determine the weight given to recent data, and therefore, the forecasts stability

Question 42

what is a moving average?

Answer 42

calculates the average of a fixed number of past data points to smooth out short-term fluctuations and highlight long-term trends

Question 43

what is regression analysis?

Answer 43

uses relationships between variables to project future values

Question 44

what is the sum of squared errors (SSE)?

Answer 44

a measure of the accuracy of a forecast/trend line by showing how much the data points deviate from the predicted values

Question 45

what does a low SSE indicate?

Answer 45

the forecast/model is a good fit for the data

Question 46

how do you calculate the inter-relation of variables?

Answer 46

calculate the correlation coefficient (r)

Question 47

what does r represent?

Answer 47

the correlation coefficient (used to measure inter-relation of variable)

Question 48

what does it mean if r = 1?

Answer 48

positive correlation between the variables

Question 49

what does it mean if r = -1?

Answer 49

perfect negative correlation between the variables

Question 50

what does it mean if r = 0?

Answer 50

no correlation between the variables

Question 51

what is the excel function to calculate slope?

Answer 51

=SLOPE(known_y's, known_x's)

Question 52

what is the excel function to calculate intercept?

Answer 52

=INTERCEPT(known_y's, known_x's)