- A research student is investigating the maximum weight, \(y\) grams, of sugar that will dissolve in 100 grams of water at various temperatures, \(x ^ { \circ } \mathrm { C }\), where \(10 \leqslant x \leqslant 80\)
The research student calculated the regression line of \(y\) on \(x\) and found it to be
$$y = 151.2 + 2.72 x$$
- Give an interpretation of the gradient of the regression line.
- Use the regression line to estimate the maximum weight of sugar that will dissolve in 100 grams of water when the temperature is \(90 ^ { \circ } \mathrm { C }\).
- Comment on the reliability of your estimate, giving a reason for your answer.
Using the regression line of \(y\) on \(x\) and the following summary statistics
$$\sum y = 3119 \quad \sum y ^ { 2 } = 851093 \quad \sum x ^ { 2 } = 24500 \quad n = 12$$
- show that the product moment correlation coefficient for these data is 0.988 to 3 decimal places.
The research student's supervisor plotted the original data on a scatter diagram, shown on page 23
With reference to both the scatter diagram and the correlation coefficient,
- discuss the suitability of a linear regression model to describe the relationship between \(x\) and \(y\).
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