Pearson product moment correlation
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1. The document discusses the relationship between two variables and defines correlation coefficients ranging from 0 to 1 to indicate the strength of their relationship. 2. It then provides an example of a fruit shake store owner studying the correlation between temperature and sales over 12 summer days. Data is presented on the temperature, sales, and calculations for correlation analysis. 3. The results of the correlation analysis show a significant association between temperature and total sales, indicating higher temperatures are correlated with increased fruit shake sales.
Pearson product moment correlation
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- 11. Coefficient Relationship 0.00 No correlation, no relationship Very low correlation, almost negligible relationship Slight correlation, definite but small relationship Moderate correlation, substantial relationship High correlation, marked relationship Very high correlation, very dependable relationship Perfect correlation, perfect relationship
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- 13. Subjects are randomly selected. Both populations are normally distributed
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- 16. When the null hypothesis has been rejected for a specific significance level, there are possible relationships between X and Y variables: 1. There is a direct cause-and-effect relationship between the two variables. 2. There is a reverse cause-and-effect relationship between the two variables. 3. The relationship between the two variables may be caused by the third variable. 4. There maybe a complexity of interrelationship among many variables. 5. The relationship between the two variables may be coincidental.
- 17. The owner of a chain of fruit shake stores would like to study the correlation between atmospheric temperature and sales during the summer season. A random sample of 12 days is selected with the results given as follows:
- 18. DAY TOTAL SALES 1 147 2 76 143 3 78 147 4 84 168 5 90 206 6 83 155 7 93 192 8 94 211 9 97 209 10 85 187 11 88 200 12 82 150
- 19. 140 150 160 170 180 190 200 210 220 75 80 85 90 95 100 TOTALSALES TEMPERATURE
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- 21. DAY X Y X2 Y2 XY 1 79 147 6,241 21,609 11,613 2 76 143 5,776 20,449 10,868 3 78 147 6,084 21,609 11,466 4 84 168 7,056 28,224 14,112 5 90 206 8,100 42,436 18,540 6 83 155 6,889 24,025 12,865 7 93 192 8,649 36,864 17,856 8 94 211 8,836 44,521 19,834 9 97 209 9,409 43,681 20,273 10 85 187 7,225 34,969 15,895 11 88 200 7,744 40,000 17,600 12 82 150 6,724 22,500 12,300 TOTAL
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- 25. Since the null hypothesis has been rejected, we can conclude that there is evidence that shows significant association between the atmospheric temperature and the total sales of fruit shake.