MAT201

MAT201: Module 5 Case Study

MAT201: Module 5 Case Study

Requirement No. 1

Model Summary b

Model

R

R-Square

Adjusted-R-Square

Standard Error of the Estimate

Change Statistics

R-Square Change

F Change

Degree of Freedom 1

Degree of Freedom 2

Significance F Change

1

.967 a

.935

.927

1.90061

.935

115.162

1

8

.000

In view of given model summary table, it is indicated that values of R Square and adjusted R Square are 0.935 and 92.7% respectively, which shows that there is strong association of dependent variable Y with the independent variable X. Moreover, for further clarity, it is vital to consider the below table:

ANOVA b

Model

Sum of Squares

Degree of Freedom

Mean Square

F

Significance

1

Regression

416.002

1

416.002

115.162

.000 a

Residual

28.898

8

3.612

Total

444.900

9

The ANOVA table presents that the significance level is below 0.05, thus, we can be said that the regression model is statistically significant. The key objective of the regression model is the prediction. Since as we expect that much of the variation of the output variable is explained by the input variables, we can use the model to obtain values ??of Y corresponding to X values ??that were not among the data. This is called the prediction and, in general, use X values ??that are within this range studied. Using values ??outside this range is called extrapolation and should be used very carefully, because the model cannot be adopted right out of the range studied. In addition to this, it is also used for the estimation of parameters; it gives a model and a set of data related to response and predictor variables, parameter estimation or model fit to the data is used to obtain mean values or estimates for the parameters.

Coefficients a

Model

Un-standardized Coefficients

Standardized Coefficients

t

Significance

Collinearity Statistics

B

Standard Error

Beta

Tolerance

Variance Inflation Factor

1

(Constant)

- 1.102

.606

- 1.819

.106

X

1.996

.186

.967

10.731

.000

1.000

1.000

In addition to this, the coefficients table indicates that the level of significance of independent variable X is statistically significant because the value is under 0.05. For that reason, it can be said that there is an association of independent variable X with the dependent variable Y. Moreover, the beta value of independent variable X is positive that is 1.996, thus, it can be said that there is positive association between X and Y that is if X increase then Y will also increase.

Regression Equation

Y = a + b X

Y = (- 1.102) + 1.996 X

Predicted Value of Y when X = - 2

Y = (- 1.102) + (1.996) (- 2)

Y = (- 1.102) + -3.992

Y = - 5.094

Predicted Value of Y when X = 4

Y = (- 1.102) + (1.996) (- 4)

Y = (- 1.102) + 7.984

Y = 6.882

Requirement No. 2

Model Summary b

Model

R

R-Square

Adjusted-R-Square

Standard Error of the Estimate

Change Statistics

R-Square Change

F Change

Degree of Freedom 1

Degree of Freedom 2

Significance F Change

1

.797 a

.634

.589

6.82715

.634

13.884

1

8

.006

The above presents that the values of R Square and adjusted R Square are 63.4 and 58.9% respectively; this indicates that there is strong association of dependent variable that is exam score with the independent variable that is hours studied.

ANOVA b

Model

Sum of Squares

Degree of Freedom

Mean Square

F

Significance

1

Regression

647.120

1

647.120

13.884

.006 a

Residual

372.880

8

46.610

Total

1020.000

9

The table presented above shows that the level of significance is less than 0.05 that is 0.006; therefore, the regression model is valid.

Coefficients a

Model

Un-standardized Coefficients

Standardized Coefficients

t

Significance

Collinearity Statistics

B

Standard Error

Beta

Tolerance

Variance Inflation Factor

1

(Constant)

68.994

5.539

12.456

.000

X

4.525

1.214

.797

3.726

.006

1.000

1.000

Besides it, the coefficients table reflects that the significance ...