Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

math 105 > midterm 2 > Flashcards

midterm 2 Flashcards

1
Q

what are the formulas for regression?

A
  • 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)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is the formula for spearman’s coefficient?

A

s = 1 - 6ΣD^2 / n(n^2 - 1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

what is the formula for exponential smoothing?

A

F(t+1) = αy(t) + (1 - α)F(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what is the formula to calculate simple averages

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

what is the formula to calculate moving averages?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

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

A
  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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

what is the formula for the correlation coefficient?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

what are variables?

A

numbers that can change

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

what does y represent?

A

the value on the vertical axis (y-axis)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

what does x represent?

A

the value on the horizontal axis (x-axis)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what does m represent?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

what does b represent?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

what does n represent?

A

the number of data points

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what does Σx mean?

A

the sum of all the x variables

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what does Σy mean?

A

the sum of all the y variables

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

what does Σxy mean?

A

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)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

what does Σx^2 mean?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

what does Σy^2 mean?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

what does (Σx)^2 mean?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

what does (Σy)^2 mean?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

what does ȳ represent?

A

the average of all y-values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

what does x̄ represent?

A

the average of all x-values

23
Q

what does S represent?

A

spearmans coefficient (always between -1 and 1)

24
Q

what does it mean if S = 1?

A

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

25
Q

what does it mean of S = -1?

A

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

26
Q

what does it mean of S = 0?

A

there’s no relationship between the ranks

27
Q

what does D represent?

A

the difference between the ranks of each pair of items

28
Q

what does ΣD^2 mean?

A

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

29
Q

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

A

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

30
Q

what does it mean if S is close to 1?

A

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

31
Q

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

A

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

32
Q

what does it mean if S is near 0?

A

there’s little to no rank correlation

33
Q

what does F(t+1) represent?

A

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

34
Q

what does α represent?

A

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

35
Q

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

A

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

36
Q

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

A

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

37
Q

what does Y(t) represent?

A

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

38
Q

what does F(t) represent?

A

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

39
Q

what is the line of best fit?

A

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

40
Q

what is the formula to calculate line of best fit?

A

y = mx + b

41
Q

what is exponential smoothing?

A

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

42
Q

what is a moving average?

A

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

43
Q

what is regression analysis?

A

uses relationships between variables to project future values

44
Q

what is the sum of squared errors (SSE)?

A

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

45
Q

what does a low SSE indicate?

A

the forecast/model is a good fit for the data

46
Q

how do you calculate the inter-relation of variables?

A

calculate the correlation coefficient (r)

47
Q

what does r represent?

A

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

48
Q

what does it mean if r = 1?

A

positive correlation between the variables

49
Q

what does it mean if r = -1?

A

perfect negative correlation between the variables

50
Q

what does it mean if r = 0?

A

no correlation between the variables

51
Q

what is the excel function to calculate slope?

A

=SLOPE(known_y’s, known_x’s)

52
Q

what is the excel function to calculate intercept?

A

=INTERCEPT(known_y’s, known_x’s)

53
Q
A

math 105 (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions