bivariate analysis linear regression chi test

7/27/2019 Bivariate Analysis Linear Regression Chi Test

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Bivariate Analysis

(a)Correlation using Linear Regression

(Fitting a straight line between two Scalar Variables)

Use dataset modified_class_example



Is there a relationship between salaries and

Student Age?



Go to ChartBuilder->Scatter/Dot

Select Student Age onto horizontal axis and Salary on vertical one



Is there a relationship between Student Age and Expected Marks?



Can we forecast a relationship between Student age and Salaries?

YES. Use linear regression. That is fit a straight line between Student

Age and Salaries.

Example:

Y = ax + b

X is the Independent Variable

Y is the Dependent Variable

b

Gradient a

X

Y Y = aX + b



Analyse -> Regression -> Linear

Model Summaryb

Model

R R Square

Adjusted R

Square

Std. Error of the

Estimate

i

m

n

i

n

1 .964a .930 .928 2120.38027

a. Predictors: (Constant), Student Age

b. Dependent Variable: Monthly Salary



R = Pearson Coefficient (-1, 1)

-1 = Negative perfect

1= Positive Perfect

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta

1 (Constant) -424.000 1625.122 -.261 .796

Student Age 996.417 50.752 .964 19.633 .000

a. Dependent Variable: Monthly Salary

b = -424.0

a = 996.417

Sig. less than 0.05 for a, shows good correlation and not by chance

Y = aX + b

Salary = 996.417 x Student Age – 424.0



Correlation between Categorical or Nominal variables

(Chi-Square Test)

Is there an Association/Relationship between Gender andMotivation?

Are males and females motivated to the same degree?

Use of Contingency tables



Analyse -> Descriptive -> Crosstabs

(Switch Display Clustered Bar on)

Statistics button



Cell button

Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

Student Gender * How

motivated is student?

31 100.0% 0 .0% 31 100.0%



Student Gender * How motivated is student? Crosstabulation

How motivated is student?

Total

Somewhat

Motivated Well Motivated Very Motivated

Student Gender male Count 12 1 5

Expected Count 7.5 2.9 7.5 18

% within Student Gender 66.7% 5.6% 27.8% 100.0

% within How motivated is

student?

92.3% 20.0% 38.5% 58.1

% of Total 38.7% 3.2% 16.1% 58.1

Female Count 1 4 8




student?

7.7% 80.0% 61.5% 41.9

% of Total 3.2% 12.9% 25.8% 41.9

Total Count 13 5 13




student?

100.0% 100.0% 100.0% 100.0

% of Total 41.9% 16.1% 41.9% 100.0

Expected frequencies E(i,j) = R(i) C(j)/ N

Chi-Square Tests

Value df

Asymp. Sig. (2-

sided)

Pearson Chi-Square 11.287a 2 .004

Likelihood Ratio 12.787 2 .002

Linear-by-Linear Association 7.490 1 .006

N of Valid Cases 31

a. 2 cells (33.3%) have expected count less than 5. The minimum

expected count is 2.10.will comment on this later……….



Sig. is less than 0.05 (5%) This means that the probability of the values (Count) in the above

table occurring by chance is less than 5%. Therefore there is a significant association/

relationship between gender and Motivation.They are not independent.Some times this test is

also called the chi test for independence.

See diagram (Females are more motivated)

bivariate analysis linear regression chi test

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