1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

2. Schedule of readings This Monday
Before our fourth and final exam (December 5th)
OpenStax
Chapters 1 – 13 (Chapter 12 is emphasized)
Plous
Chapter 17: Social Influences
Chapter 18: Group Judgments and Decisions

3. By the end of lecture today 12/2/16
Review for Exam 4
No new material
Review homeworks
Clicker Questions

4. with a letter somewhere between
Homework:
No more homework!!
Please click in
My last name starts
with a letter somewhere between
A. A – D
B. E – L
C. M – R
D. S – Z

5. Just one quick favor… Please use your phone or laptop
Please take just a minute to complete
Course Evaluations online…..
Check your for a link or go to…
tceonline.oia.arizona.edu

6. Correlation - What do we need to define a line
If you probably make this much
Expenses per year
Yearly Income
Y-intercept = “a” (also “b0”) Where the line crosses the Y axis
Slope = “b” (also “b1”) How steep the line is
If you spend this much
The predicted variable goes on the “Y” axis and is called the dependent variable
The predictor variable goes on the “X” axis and is called the independent variable

7. Describe relationship Regression line (and equation) r = 0.71
Rory’s Regression: Predicting sales from number of visits (sales calls)
Describe relationship
Regression line (and equation)
r = 0.71
Correlation: This is a strong positive correlation. Sales tend to increase as sales calls increase
Predict using regression line
(and regression equation)
b = (slope)
Slope: as sales calls increase by 1, sales should increase by
Dependent
Variable
Intercept: suggests that we can assume each salesperson will sell at least systems
a = (intercept)
Independent
Variable
Review

8. Review 50% is explained so the other 50% has yet to be explained
(0.71 > 0.632)
Review

9. Summary
Intercept: suggests that we can assume each salesperson will sell at least systems
Slope: as sales calls increase by one, more systems should be sold
Review

10. Regression Analysis – Least Squares Principle
When we calculate the regression line we try to:
minimize distance between predicted Ys and actual (data) Y points (length of green lines)
remember because of the negative and positive values cancelling each other out we have to square those distance (deviations)
so we are trying to minimize the “sum of squares of the vertical distances between the actual Y values and the predicted Y values”

11. Homework Review

12. For each additional hour worked, weekly pay will increase by $6.09
+0.92
positive
strong
The relationship between
the hours worked and weekly pay is a strong positive correlation.
This correlation is significant, r(3) = 0.92; p < 0.05 up
down
55.286
6.0857
y' = x
207.43
85.71
or 84%
84% of the total variance of “weekly pay” is accounted for by “hours worked”
For each additional hour worked, weekly pay will increase by $6.09

13. 400
380
360
Wait Time
340
320
300
280 4 5 6 7 8
Number of Operators

14. No we do not reject the null
Critical r = 0.878
No we do not reject the null
-.73
negative
strong
The relationship between
wait time and number of operators working is negative and moderate. This correlation is not
significant, r(3) = 0.73; n.s.
number of operators increase, wait time decreases
458
-18.5
y' = -18.5x + 458
365 seconds
328 seconds
or 54%
The proportion of total variance of wait time accounted for by number of
operators is 54%.
For each additional operator added, wait time will decrease by 18.5 seconds

15. 39 36 33 30 27 24 21
Percent of BAs
Median Income

16. Percent of residents with a BA degree
Critical r = 0.632
Yes we reject the null
Percent of residents with a BA degree 10 8
0.8875
positive
strong
The relationship between
median income and percent of residents with BA degree is strong and positive. This correlation is significant, r(8) = 0.89; p < 0.05.
median income goes up so does percent of residents who have a BA degree
3.1819
0.0005
y' = x
25% of residents
35% of residents
or 78%
The proportion of total variance of % of BAs accounted for by
median income is 78%.
For each additional $1 in income, percent of BAs increases by .0005

17. 30 27 24 21 18 15 12
Crime Rate
Median Income

18. No we do not reject the null
Critical r = 0.632
No we do not reject the null
Crime Rate 10 8
negative
moderate
The relationship between
crime rate and median income is negative and moderate. This correlation is not significant,
r(8) = -0.63; p < n.s. [ is not bigger than critical of 0.632] .
median income goes up, crime rate tends to go down
4662.5
y' = x
2,417 thefts
1,418.5 thefts
.396 or 40%
The proportion of total variance of thefts accounted for by
median income is 40%.
For each additional $1 in income, thefts go down by .0499

19. Review
Sheet

20. As variability goes down, it is easier to reject the null
decrease
narrower
As variability goes down, it is easier to reject the null
ANOVA

21. .9918 .4918 .5000 40 z = 52-40 5 z = 2.4 Go to table .4918 Add area
Lower half
= .9918
also fine: %
.9918
.4918
.5000
z =2.4 40

22. As variability goes down, it is easier to reject the null
decrease
narrower
As variability goes down, it is easier to reject the null
ANOVA
99.18%

23. Interval True experiment
Interval
True experiment
Income x Education, would allow the most accurate predictions because this relationship has the largest correlation coefficient of 0.85
This would be statistically significant with alpha of 0.05 because p = 0.02 so p < 0.05
NOT statistically significant with alpha of 0.01 because p = 0.02; p is not < .01

24. IQ x Age, would allow the weakest predictions because this relationship has the smallest correlation coefficient of -0.02
0.91
No because 0.91 is not less than 0.05
Education x Income is the only one that is significant; p = 0.02 so p < 0.05
None because none have p < .01 r2

25. Standard error of the estimate
Because it is a measure of the amount of error in the regression line (average of residuals)
81% because .92 = .81
19% because
100% – 81% =19%
The correlation between the heights of mothers and their daughters is moderate, positive and statistically significant, r(28) = 0.60; p< 0.05
36% because .62 = .36
64% because
100% – 36% =64%
75% because 100% – 25% =75% (note: .52 = .25)

26. 0.92
0.922 = .8464
6.0857
.8464 = 0.922
.1536 =
6.0857
55.286
Y’ = x
$6.09
residual

27. r r2 b r2 b a

28. -1 +1
+1 (or 100%)
anything
anything
+1 (or 100%)
anything
anything
anything
anything
any positive number
Y’ = x

29. A deviation score is a difference score
from actual score to the mean. A residual is the difference actual score and predicted score (which is mean)
Standard deviation is
like the mean of deviation scores; standard error of estimate is like
mean of residual scores
How far away is each score from the regression line (like mean of subgroup)

30. Do not reject the null hypothesis because observed F is less than one

31. Please hand
in your homework

32. Today we will be reviewing for the test using clicker questions.

33. What if we were looking to see if our stop-smoking program affects
peoples‘ desire to smoke. What would null hypothesis be?
a. Can’t know without knowing the dependent variable
b. The program does not work
c. The programs works
d. Comparing the null and alternative hypothesis
Correct

34. Correct
Which of the following is a Type I error:
a. We conclude that the program works when it fact it doesn’t
b. We conclude that the program works when in fact it does
c. We conclude that the program doesn’t work when in fact it does
d. We conclude that the program doesn’t work when in fact it doesn’t

35. What is the null hypothesis of a correlation coefficient. a
What is the null hypothesis of a correlation coefficient?  a. It is zero (nothing going on) b. It is less than zero c. It is more than zero d. It equals the computed sample correlation
Correct

36. Let’s try one
Winnie found an observed correlation coefficient of 0, what should she conclude?
a. Reject the null hypothesis
b. Do not reject the null hypothesis
c. Not enough info is given
Correct

37. In the regression equation, what does the letter "a" represent. a
In the regression equation, what does the letter "a" represent?  a. Y intercept b. Slope of the line c. Any value of the independent variable that is selected d. None of these
Correct

38. Correct Assume the least squares equation is Y’ = 10 + 20X.
What does the value of 10 in the equation indicate?  a. Y intercept b. For each unit increased in Y, X increases by 10 c. For each unit increased in X, Y increases by 10 d. None of these .
Correct

39. In the least squares equation,  Y’  = X the value of 20 indicates  a. the Y intercept. b  slope (so for each unit increase in X, Y’ increases by 20). c. slope (so for each unit increase in Y’, X increases by 20). d. none of these.
Correct

40. In the equation Y’ = a + bX, what is Y’. a. Slope of the line b
In the equation  Y’  = a + bX, what is  Y’ ?  a. Slope of the line b. Y intercept C. Predicted value of Y, given a specific X value d. Value of Y when X = 0
Correct

41. According to the Central Limit Theorem, which is false?
As n ↑ x will approach µ b.
As n ↑ curve will approach normal shape c.
As n ↑ curve variability gets larger
Correct
As n ↑ d.

42. coefficient of determination = r2
If the coefficient of determination is 0.80, what percent of variation is explained?  a. 20% b. 90% c. 64% d. 80%
Correct
coefficient of determination = r2
What percent of variation is not explained?  a. 20% b. 90% c. 64% d. 80%
Correct

43. Which of the following represents a significant finding:
a. p < 0.05
b. t(3) = 0.23; n.s.
c. the observed t statistic is nearly zero
d. we do not reject the null hypothesis
Correct

44. Correct
If r = 1.00, which inference cannot be made? a. The dependent variable can be perfectly predicted by the
independent variable b. This provides evidence that the dependent variable is
caused by the independent variable
c. All of the variation in the dependent variable can be
accounted for by the independent variable d. Coefficient of determination is 100%.

45. Let’s try one
In a regression analysis what do we call the variable used to
predict the value of another variable? 
a. Independent
b. Dependent
c. Correlation
d. Determination
Correct

46. What can we conclude if the coefficient of determination is 0.94?  a.  r2 = 0.94 b. direction of relationship is positive c.  94% of total variation of one variable is explained by variation
in the other variable. d.  Both A and C
Correct

47. Which of the following statements regarding the coefficient of correlation
is true? 
a. It ranges from -1.0 to +1.0
b. It measures the strength of the relationship between two variables
c. A value of 0.00 indicates two variables are not related
d. All of these
Correct

48. coefficient of correlation = r coefficient of determination = r2
What does a coefficient of correlation of 0.70 infer? (r = +0.70) 
a. Almost no correlation because 0.70 is close to 1.0
b. 70% of the variation in one variable is explained by the other
c. Coefficient of determination is 0.49
d. Coefficient of nondetermination is 0.30
Correct
coefficient of correlation = r
coefficient of determination = r2

49. If r = 0.65, what does the coefficient of determination equal?  a. 0.194 b. 0.423 c. 0.577 d. 0.806
Correct

50. If the coefficient of correlation is 0
If the coefficient of correlation is 0.60, what percent of variation is not explained?  a. 20% b. 90% c. 64% d. 80%
Correct

51. If the coefficient of determination is 0
If the coefficient of determination is 0.20, what percent of variation is not explained?  a. 20% b. 90% c. 64% d. 80%
Correct

52. What is the measure that indicates how precise a prediction of Y is
based on X or, conversely, how inaccurate the prediction might be?  a. Regression equation b. Slope of the line c. Standard error of estimate d. Least squares principle
Correct

53. Let’s try one
Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?
a. the means are the same, so the t-test would yield the same results.
b. the means are the same, but the variability would increase so
it would be harder to reject the null hypothesis. c. the means are the same, but the variability would decrease so
it would be easier to reject the null hypothesis.
Correct

54. Agnes compared the heights of the women’s gymnastics team and the scores they got. If she doubled the number of players measured, but ended up with the same correlation (r) what effect would that have on the results?
Let’s try one
a. the r is the same, so the conclusion would be the same
b. the r is the same, but with more people, degrees of freedom (df) would go up and it would be harder to reject the null hypothesis. c. the r is the same, but with more people, degrees of freedom (df) would go up and it would be easier to reject the null hypothesis.
Correct

55. Standard error of the estimate (line) Correct
Which of the following is true about the standard error of estimate?  a. It is a measure of the accuracy of the prediction b. It is based on squared vertical deviations between Y and Y’ c. It cannot be negative d. All of these
Correct
Standard error of the estimate:
a measure of the average amount of predictive error
the average amount that Y’ scores differ from Y scores
a mean of the lengths of the green lines

56. Standard error of the estimate (line) Correct
If all the plots on a scatter diagram lie on a straight line, (perfect correlation) what is the standard error of estimate?  a. - 1 b. +1 c. 0 d. Infinity
Correct
Standard error of the estimate:
a measure of the average amount of predictive error
the average amount that Y’ scores differ from Y scores
a mean of the lengths of the green lines

57. Let’s try one
Scatterplot A
Scatterplot B
Scatterplot C
Which of these correlations would be most likely to have the highest positive value for r? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given
Correct

58. Let’s try one
Scatterplot A
Scatterplot B
Scatterplot C
Which of the these scatterplots will have the smallest “y intercept”? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given
Correct

59. Let’s try one
Scatterplot A
Scatterplot B
Scatterplot C
Which of the these correlations would be most likely to represent the correlation between salary and expenses? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given
Correct

60. Let’s try one
Which of the following correlations would allow you the most accurate predictions?
a. r = b. r = c. r = d. r =
Correct

61. Let’s try one
After duplicate correlations have been discarded and trivial correlations have been ignored, there remain
a. two correlations b. three correlations c. six correlations d. nine correlations
Correct

62. Let’s try one
Which of the following conclusions can not be made from the data in the matrix?
a. There is a significant correlation between Science and Reading
b. There is a significant correlation between Math and Reading
c. There is a significant correlation between Math and Science
Correct

63. Winnie found an observed t of .04, what should she conclude?
Let’s try one
Winnie found an observed t of .04, what should she conclude?
(Hint: notice that .04 is less than 1)
a. Reject the null hypothesis
b. Do not reject the null hypothesis
c. Not enough info is given
correct x
small observed t score

64. Thank you ! Thank you for a wonderful semester!
and good luck with your studies
See you at the final exam . .