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Lab
TA:_______________ID:_________________Name:_________
__________
Soc 3811 Basic Social Statistics
Extra Credit
A total of 20 points
1. The following table presents the total sample size and the
percentage distribution of a grouped variable, “Hours of
Shopping this Year.” Calculate the mean and the variance. Note
that you need to find “frequency (fi)”, “midpoint (Yi)”, and
“deviation (di)” for each row before you can get the mean and
the variance.
Hours Shopping
Percentage
(%)
Frequency
(fi)
Midpoint
(Yi)
Deviation
di2
di2(fi)
1-4
5
5-8
25
9-12
15
13-16
30
17-20
5
21-24
20
Total
100.0
550
Mean___________ Variance___________
2. One of the Stat’s TA’s believes that cats are more popular
than dogs. Test the hypothesis using the data within the data
tables provided below.
Cats
Popularity
Freq
Percent
Cum. %
low
15
75
75
high
5
25
100
Total: 20
Dogs
Popularity
Freq
Percent
Cum. %
low
22
68.75
68.75
high
10
45.45
100
Total: 32
1: State the research and null hypothesis in symbolic form.
2: Perform a T-test.
3: Find the critical value of T relative to the .05 alpha level.
4: Make a decision relative to the null hypothesis and interpret
the result.
3. The following equation is a predicted regression line based
on an analysis of a sample of 2,500 people. “Happiness” is the
dependent continuous variable measured by a 100 point
happiness scale. Income is a dummy variable, 0 for low-income,
1 for middle-income, and 2 for upper-income.
Happiness = a + b * Income
Here is the STATA output:
Happiness
Coefficient
St. Error
t
P>t
Income
22.45
4.76
7.65
.000
Constant
19.1
4.09
2.25
.029
Observations = 2500 F(1, 2498) = 13.32 Prob > F=.0001
R^2 = .217 Adj. R^2= .201
Answer the following questions.
1. Are the variables happiness and income related, and if so, by
how much? How do you know this?
2. What is the strength of this relationship?
Happiness = a + b * Income+ b * Health - b * Age
The above equation is a predicted multivariable regression line
based on an analysis of a sample of 2,500 people. “Happiness”
is the dependent continuous variable measured by a 100 point
happiness scale. Health is a continuous measure, scored 0 (poor
health) to 10 (excellent health). Income is a dummy variable, 0
for low-income, 1 for middle- to upper-income. Age is a
continuous measure and is measured in years.
Here is the STATA.
Happiness
Coefficient
St. Error
t
P>t
Income
15.6
3.76
3.65
.001
Health
10.4
1.77
3.09
.001
Age
-5.9
.87
2.76
.01
Constant
19.1
4.09
2.25
.029
Observations = 2500 F(1, 2498) = 9.44 Prob > F=
.0001 R^2 = .381 Adj. R^2= .341
Answer the following.
3. Compare the coefficients from this model to the bivariate
model above. How are they different, and why do you think they
are different? Which is a better model?
4. Write the predicted equations for both the bivariate and
multivariate regressions. Use variable names instead of x and y.
5. Your friend is planning on making a New Year’s resolution to
be happier next year. What would you recommend her to focus
on?
4. The following table depicts data about the relationship
between hours played per week on a video game (Y) and
experience level growth in the game (x).
Hours playing video game per week
Experience level growth in game
Mean
S.D.
Hours playing video game per week
1.00
.88
21.2
3.9
Experience level growth in game
1.00
9
2.3
N = 154
1. Find the coefficients.
R =
b =
β =
2. Find the constant.
a =
3. Find the equation.
=
4. Fill out the table for ANOVA for Regression
Sum of Squares
Degrees of freedom
Mean Squares
F-statistic
Regression
Error
Total
Interpret the result of the F-statistic: can you reject the null at
the alpha level of .05?

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Lab TA_______________ID_________________Name__________________.docx

  • 1. Lab TA:_______________ID:_________________Name:_________ __________ Soc 3811 Basic Social Statistics Extra Credit A total of 20 points 1. The following table presents the total sample size and the percentage distribution of a grouped variable, “Hours of Shopping this Year.” Calculate the mean and the variance. Note that you need to find “frequency (fi)”, “midpoint (Yi)”, and “deviation (di)” for each row before you can get the mean and the variance. Hours Shopping Percentage (%) Frequency (fi) Midpoint (Yi) Deviation di2 di2(fi) 1-4 5
  • 3. 20 Total 100.0 550 Mean___________ Variance___________ 2. One of the Stat’s TA’s believes that cats are more popular than dogs. Test the hypothesis using the data within the data
  • 4. tables provided below. Cats Popularity Freq Percent Cum. % low 15 75 75 high 5 25 100 Total: 20 Dogs Popularity Freq Percent Cum. % low 22 68.75 68.75 high 10 45.45 100 Total: 32 1: State the research and null hypothesis in symbolic form.
  • 5. 2: Perform a T-test. 3: Find the critical value of T relative to the .05 alpha level. 4: Make a decision relative to the null hypothesis and interpret the result. 3. The following equation is a predicted regression line based on an analysis of a sample of 2,500 people. “Happiness” is the dependent continuous variable measured by a 100 point happiness scale. Income is a dummy variable, 0 for low-income, 1 for middle-income, and 2 for upper-income. Happiness = a + b * Income Here is the STATA output: Happiness
  • 6. Coefficient St. Error t P>t Income 22.45 4.76 7.65 .000 Constant 19.1 4.09 2.25 .029 Observations = 2500 F(1, 2498) = 13.32 Prob > F=.0001 R^2 = .217 Adj. R^2= .201 Answer the following questions. 1. Are the variables happiness and income related, and if so, by how much? How do you know this? 2. What is the strength of this relationship? Happiness = a + b * Income+ b * Health - b * Age The above equation is a predicted multivariable regression line based on an analysis of a sample of 2,500 people. “Happiness” is the dependent continuous variable measured by a 100 point happiness scale. Health is a continuous measure, scored 0 (poor
  • 7. health) to 10 (excellent health). Income is a dummy variable, 0 for low-income, 1 for middle- to upper-income. Age is a continuous measure and is measured in years. Here is the STATA. Happiness Coefficient St. Error t P>t Income 15.6 3.76 3.65 .001 Health 10.4 1.77 3.09 .001 Age -5.9 .87 2.76 .01 Constant 19.1 4.09 2.25 .029 Observations = 2500 F(1, 2498) = 9.44 Prob > F= .0001 R^2 = .381 Adj. R^2= .341 Answer the following.
  • 8. 3. Compare the coefficients from this model to the bivariate model above. How are they different, and why do you think they are different? Which is a better model? 4. Write the predicted equations for both the bivariate and multivariate regressions. Use variable names instead of x and y. 5. Your friend is planning on making a New Year’s resolution to be happier next year. What would you recommend her to focus on? 4. The following table depicts data about the relationship between hours played per week on a video game (Y) and experience level growth in the game (x). Hours playing video game per week Experience level growth in game Mean S.D. Hours playing video game per week 1.00 .88 21.2 3.9 Experience level growth in game 1.00 9
  • 9. 2.3 N = 154 1. Find the coefficients. R = b = β = 2. Find the constant. a = 3. Find the equation. = 4. Fill out the table for ANOVA for Regression Sum of Squares Degrees of freedom Mean Squares F-statistic Regression
  • 10. Error Total Interpret the result of the F-statistic: can you reject the null at the alpha level of .05?