7. A number of people were asked to guess the calorific content of 10 foods. The
mean \(s\) of the guesses for each food and the true calorific content \(t\) are given in the table below.
| Food | \(t\) | \(s\) |
| Packet of biscuits | 170 | 420 |
| 1 potato | 90 | 160 |
| 1 apple | 80 | 110 |
| Crisp breads | 10 | 70 |
| Chocolate bar | 260 | 360 |
| 1 slice white bread | 75 | 135 |
| 1 slice brown bread | 60 | 115 |
| Portion of beef curry | 270 | 350 |
| Portion of rice pudding | 165 | 390 |
| Half a pint of milk | 160 | 200 |
[You may assume that \(\Sigma t = 1340 , \Sigma s = 2310 , \Sigma t s = 396775 , \Sigma t ^ { 2 } = 246050 , \Sigma s ^ { 2 } = 694650\).]
- Draw a scatter diagram, indicating clearly which is the explanatory (independent) and which is the response (dependent) variable.
- Calculate, to 3 significant figures, the product moment correlation coefficient for the above data.
- State, with a reason, whether or not the value of the product moment correlation coefficient changes if all the guesses are 50 calories higher than the values in the table.
The mean of the guesses for the portion of rice pudding and for the packet of biscuits are outside the linear relation of the other eight foods.
- Find the equation of the regression line of \(s\) on \(t\) excluding the values for rice pudding and biscuits.
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[You may now assume that \(S _ { t s } = 72587 , S _ { t t } = 63671.875 , \bar { t } = 125.625 , \bar { s } = 187.5\).] - Draw the regression line on your scatter diagram.
- State, with a reason, what the effect would be on the regression line of including the values for a portion of rice pudding and a packet of biscuits.
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