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Pearson's Correlation Coefficient and Regression Equation

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The following table represents data involving direct labour costs (in Rands) and the batch size (in units) produced by a small manufacturing concern that specialises in a single product.

BATCH SIZE (units) LABOUR COSTS (Rands)
15 200
18 240
21 290
23 300
26 380
28 370
32 400

1. Determine Pearson's correlation coefficient and comment on the value obtained.

2. Obtain a regression equation representing the above data.

3. Estimate the production batch size for a direct labour cost of R350-00.

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Solution Summary

This solution determines Pearson's correlation coefficient and regression equation from an ANOVA analysis. It also uses the regression equation to estimate the product batch size for a specific direct labour cost.

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Statistics: Pearson Correlation, Regression Equation

See attached file for tables.

Problem Set 1: Chapter 16, problems 2, 6c, 14; Chapter 17, problem 14

2. What information is provided by the numerical value of the Pearson correlation?

6. For the following scores,

X Y
1 5
2 9
4 3
5 1
3 2

c. Compute a Pearson Correlation

14. It is well known that similarity. Compute a Pearson correlation for these data and determine whether there is a significant correlation between attitudes for husbands and wives. Set alpha at .05, two-tailed.

Couple Wife (X) Husband (Y)
A 11 14
B 6 7
C 16 15
D 4 7
E 1 3
F 10 9
G 5 9
H 3 8

Chapter 17

14. Problem 15 in Chapter 16 described a study examining the effectiveness of a 7-minute Screen test for Alzheimer's disease: A sample of n = 9, mean scores on the 7-minute test = M = 7, SS = 92. The cognitive test scores averaged M = 17 with SS = 236. For these data, SP = 127.

a. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score.
b. What percentage of variance in the cognitive scores is accounted for by the regression equation?
c. Does the regression equation account for a significant portion of the variance in the cognitive scores? Use Ã?¯Ã??Ã?¡ = .05 to evaluate the F-ratio.

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