In: Statistics and Probability
Open travel data file <문제> 1. Set 3 hypotheses (2 main hypotheses and one interaction hypothesis) 2. Which variable(s) are significant? and Why? 3. Which pairs of group means of travel visit are different out of three pairs in tour frequency. Which statistic did you use? 4. Use graph in order to interpret how travel frequency affects travel attitude for different sex?
sex frequency attitude
1 1 2
1 1 3
1 1 4
1 1 4
1 1 2
1 2 4
1 2 5
1 2 5
1 2 3
1 2 3
1 3 8
1 3 9
1 3 8
1 3 7
1 3 7
2 1 6
2 1 7
2 1 6
2 1 5
2 1 7
2 2 3
2 2 4
2 2 5
2 2 4
2 2 5
2 3 6
2 3 6
2 3 6
2 3 7
2 3 8
1)
Hypothesis testing can be done basis:
Let's assume sex is dependent variable & travel frequency & travel attitude determine it.
a)
H0:- Person with greater travel frequency will likely be male(Sex=1) than with less travel frequency
v/s
H1:- Not H0
b)
H0:- Person with greater attitude score will likely be male (Sex=1)than with less attitude score
v/s
H1:- Not H0
c)
H0:-There is no interaction between travel frequency & travel attitude on sex of an individual
v/s
H1:- Not H0
2)
Regression Statistics | |
Multiple R | 0.916851 |
R Square | 0.840616 |
Adjusted R Square | 0.797675 |
Standard Error | 0.660932 |
Observations | 29 |
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 2 | 62.20556 | 31.10278 | 71.20089 | 2.83235E-11 |
Residual | 27 | 11.79444 | 0.436831 | ||
Total | 29 | 74 |
Coefficients | Standard Error | t Stat | P-value | |
Intercept | 0 | #N/A | #N/A | #N/A |
travel frequency | 0.082406292 | 0.170845304 | 0.482344497 | 0.633448675 |
Travel attitude | 0.226741302 | 0.065592563 | 3.456814203 | 0.001824996 |
We see from the table above , the p-value for travel frequency is > 0.05 hence the beta coefficent is 0 and the variable is not significant.
Sex = 0.2267* travel attitude
with 84% variation explained.(R-square value).
3)
We would use t-test to compare group means and do pair wise comparisons
4)
Travel frequency is determined by blue line and as you may se ,it is same for both the gender.
Travel attitude is however higher in male than in female.