Question
To study the relationship between the number of hours spent studying per week and the marks obtained in an examination, a sample of 10 students was taken. The data is as follows:
| Study Hours (X) | 5 | 8 | 10 | 12 | 15 | 4 | 7 | 9 | 11 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|
| Marks (Y) | 55 | 70 | 75 | 80 | 90 | 50 | 65 | 72 | 78 | 85 |
(a) Calculate the Karl Pearson's coefficient of correlation between Study Hours and Marks.
(b) Determine the two regression equations (Y on X and X on Y).
(c) Predict the marks of a student who studies for 13 hours a week.
Answer :
Word Count : 554
To solve this problem using statistical techniques, we first organize the data and calculate necessary components for correlation and regression analysis. The data is: | X (Study Hours) | 5 | 8 | 10 | 12 | 15 | 4 | 7 | 9 | 11 | 14 | | --------------- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | | Y (Marks) | 55 | 70 | 75 | 80 | 90 | 50 | 65 | 72 | 78 | 85 | Step 1: Calculate sums and means $$ \sum X = 5+8+10+12+15+4+7+9+11+14 = 95 $$ $$ \sum Y = 55+70+75+80+90+50+65+72+78+85 = 720 $$ $$ \bar{X} = \frac{\sum X}{n} = \frac{95}{10} = 9.5 $$ $$ \bar{Y} = \frac{\sum Y}{n} = \frac{720}{10} = 72 $$ ________ ________ _________ _________ ________ _____ ______ _______ ________.
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To solve this problem using statistical techniques, we first organize the data and calculate necessary components for correlation and regression analysis. The data is: | X (Study Hours) | 5 | 8 | 10 | 12 | 15 | 4 | 7 | 9 | 11 | 14 | | --------------- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | | Y (Marks) | 55 | 70 | 75 | 80 | 90 | 50 | 65 | 72 | 78 | 85 | Step 1: Calculate sums and means $$ \sum X = 5+8+10+12+15+4+7+9+11+14 = 95 $$ $$ \sum Y = 55+70+75+80+90+50+65+72+78+85 = 720 $$ $$ \bar{X} = \frac{\sum X}{n} = \frac{95}{10} = 9.5 $$ $$ \bar{Y} = \frac{\sum Y}{n} = \frac{720}{10} = 72 $$ ________ ________ _________ _________ ________ _____ ______ _______ ________.
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