SPSS statistics: correlation and regression

SPSS Statistics: Correlation & Regression

Correlation & Regression

Is there a relationship between defect rate and volume? If so, is it positive or negative?

Yes, there is a relationship between defect rate and volume. The relationship is positive, such that as volume increases, so does the defect rate (.740).

Which variable is the independent and which is the dependent variable?

The independent variable (predictor) is the volume of production, and the dependent variable is the defect rate (outcome).

Write out the regression equation and sketch it on the plot.

Predicted score = Bslope X + Bconstant

Predicted score = 0.027(X) + (-97.073)

Based on a review of the plot provided, and examining two points -- 4400 and 4000, which respectively appear to hit the Y axis at 10% and 20.7%, the slope can be calculated to be

Thus, the regression equation would be:

Predicted Score = 0.027 (X) --

54% of the variability in defect rate can be explained by differences in volume.

5. What defect rate would you predict for a shift with a volume of 4000 units?

Defect Rate = 0.027 (4000) -- 97.073

= 10.927

6. What defect rate would you predict for a shift with a volume of 9000 units?

Defect Rate = 0.027 (9000) -- 97.073

= 145.927

7. Would you expect all shifts that produced 4000 items to have the same defect rate?

No. There can still be variance.

8. What would you estimate the standard deviation of the distribution of the defect rate to be for a volume of 4000 units?

The standard deviation of the intercept is 7.819

The standard deviation of the slope is .002

The Standard Error of the Estimate is 4.92.

9. If a particular shift produced 4000 items and had a defect rate of 10%, based on the regression model what would be the residual for the shift?

-.927, as the actual defect rate is .927 below the predicted defect rate based on this model.

Question 11B

1. Yes there appears to be a linear relationship between husband and wife's education.

2. The relationship between husband and wife's education appears to be positive, such that as one increases, so does the other.

3. The slope is .620 -- such that for every unit of increase in husband's education, the wife's education increases by .62.

4. The correlation coefficient (beta) is .561.

5. There are a few outliers on the scatterplot. In most of these cases they represent husbands who have higher educations than their wives.

Question 11C

1. Husband's education = .620(X)+5.341

31.4% of the variability in husband's education can be explained by wife's education.

2. Husband's education = .620(13)+5.341

= 13.401

Question 11D

1. What are the null and alternative hypotheses?

Null Hypothesis: Volume has no relation to defect rate (the slope is equal to 0).

Alternative Hypothesis: As volume increase, defect rate increases. (the slope is not equal to 0).

2. What is the population of interest? What is the sample?

All shifts at the plant in question make up the population of interest.

160 randomly selected shifts make up the sample.

3. On the basis of the output, what can you conclude about the null hypothesis?

The null hypothesis can be rejected. There is a significant linear regression between volume and defect rate and the slope is not equal to 0.

4. Can you reject the null hypothesis that the slope is 0?

Yes. The scatter plot shows a linear relationship and the regression coefficient is .740. The value of t is 13.846, indicating that the slope is 13.846 standard error units above a slope of 0, which has a significance of .000, therefore allowing one to reject the hypothesis that the slope is equal to 0.

5. Can you reject the null hypothesis that there is no linear relationship between the dependent and independent variables?

Yes. There is a relationship between the dependent and independent variables, as evidenced by the significant regression analysis and the significant correlation coefficient.

6. Can you reject the null hypothesis that the population correlation coefficient is 0?

Yes, when we reject the null hypothesis that the slope is equal to 0, this allows us to also reject the null hypothesis that the population correlation coefficient is equal to 0.

7. What would you predict the defect rate to be on a day when the volume is 4200 units? What would you predict the average defect rate to be for all days with production volumes of 4200?

Predicted Defect Rate = 0.027 (4200) -- 97.073

= 16.327

The average defect rate for all days with production volumes of 4200 would also be 16.327.

8. In what way do the two estimates of the defect rate in the question above differ?