Study

 

  

We surveyed a random sample sample from the population of North Olmsted High School juniors and seniors. We wanted to obtain data from students who maintain a job outside of school so we decided to sample juniors and seniors instead of the whole population at North Olmsted High School. If we were to sample freshman and sophomores as well, the data would be biased because most freshman and sophomores most likely don’t have a job. We surveyed a total of seventy juniors and seniors at random.


The type of test used was the linear regression


We are testing β.


 β = the slope of the population regression of the number of hours worked vs. the student’s GPA.


Ho: There is no linear correlation between number of hours worked and the student’s GPA

Ha: There is a linear correlation between number of hours worked and the student’s GPA


test-statistic: linear regression t-test=(b- β)/(Sb)


Assumptions:

Linear relationship

Multivariate normality

no or little multicollinearity

no auto-correlations

homoscedasticity

 

Regression Analysis: GPA versus HOURS WORKED 

The regression equation is
GPA = 3.12 - 0.00428 HOURS WORKED

Predictor          Coef   SE Coef      T      P
Constant         3.1223    0.1231  25.37  0.000
HOURS WORKED  -0.004275  0.008895  -0.48  0.633

S = 0.622886   R-Sq = 0.6%   R-Sq(adj) = 0.0%

Analysis of Variance

Source          DF       SS      MS     F      P
Regression       1   0.0896  0.0896  0.23  0.633
Residual Error  40  15.5195  0.3880
Total           41  15.6091

Unusual Observations

      HOURS
Obs  WORKED     GPA     Fit  SE Fit  Residual  St Resid
 10    30.0  1.7000  2.9940  0.2129   -1.2940     -2.21R
 22    35.0  2.9000  2.9726  0.2534   -0.0726     -0.13 X
 34     0.0  1.5000  3.1223  0.1231   -1.6223     -2.66R

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.

 


linear regression correlation of determination: 0.006


weak correlation r-square value is 0.00-0.49

moderate correlation r-square value: 0.50-0.80

strong correlation r-square value: 0.81-1.00


                                      

                                                  Data                                               Graphs