Assignment: Through analysis of the SPSS output, answer the following questions.

Question

Assignment: Through analysis of the SPSS output, answer the following questions. 1. What is the total sample size? 2. What is the mean income and mean number of hours worked? 3. What is the correlation coefficient between the outcome and predictor variables? Is it significant? How would you describe the strength and direction of the relationship? What it the value of R squared (coefficient of determination)? Interpret the value. Interpret the standard error of the estimate? What information does this value provide to the researcher? The model fit is determined by the ANOVA table results (F statistic = 37.226, 1,376 degrees of freedom, and the p value is.001). Based on these results, does the model fit the data? Briefly explain. (Hint: A signifi model fit.) Based on the coefficients, what is the value of the y-intercept (point at which the line of best fit crosses the y-axis)? 4. 5. 6. 9 icant finding indicates good 7.

Explanation / Answer

1.Total sample size = 378.
[From the ANOVA table, df = 377 = n – 1, thus, total sample size n = df + 1 = 378.]

2. Mean income = $1485.49
Mean working hours = 33.52
[From the descriptive statistics table]

3. Correlation between the outcome and the predictor variable= 0.3
Thus, their relationship is weak since it is near about 0 and it is positive, i.e, if one increases, the other also increases and vice versa.
Yes, it is significant.
[Correlations table]

4. R square (coefficient of determination)= 0.09.
This implies that 9% of the total variability is explained by the regression.

5. The standard error of the estimate is a measure of the accuracy of prediction made with a regression. In a scatterplot in which the S.E.of the estimate is small, one would therefore expect to see that most of the observed values cluster fairly closely to the regression line. When the S.E.of the estimate is large, one would expect to see many of the observed values far away from the regression line.

6. Critical F = Upper 5%point of F- distribution with 1 and 376 degrees of freedom
= 3.866309
F calculated > Critical F, hence we reject the null hypothesis at 5%level and conclude that the model fitted is valid and significantly explains the dependent variable.
Since p value < 0.05, we reject the null hypothesis.

7. y-intercept = 711.651 based on the constant in the regression table.

8. Regression equation :
Income = 711.651 + 23.083 * No. of working hours per week

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