Question

A study was made on the amount of converted sugar in a certain process at various temperatures. The data were coded and recorded as follows:

Temperature	Converted Sugar
1.0	8.1
1.1	7.8
1.2	8.5
1.3	9.8
1.4	9.5
1.5	8.9
1.6	8.6
1.7	10.2
1.8	9.3
1.9	9.2
2.0	10.5

1. Estimate the linear regression line.
2. Estimate the mean amount of converted sugar produced when coded temperature is 1.75.
3. Estimate the conditional standard deviation of converted sugar on temperature.
4. Estimate the correlation coefficient of converted sugar on temperature.
5. Determine and plot data, the regression line and the 90% confidence interval of the above regression equation in the same plot.

Answer 1

The following table will be useful:

	Temperature, xi	Converted Sugar, yi	xiyi	xi2	yi2
	1	8.1	8.1	1	65.61
	1.1	7.8	8.58	1.21	60.84
	1.2	8.5	10.2	1.44	72.25
	1.3	9.8	12.74	1.69	96.04
	1.4	9.5	13.3	1.96	90.25
	1.5	8.9	13.35	2.25	79.21
	1.6	8.6	13.76	2.56	73.96
	1.7	10.2	17.34	2.89	104.04
	1.8	9.3	16.74	3.24	86.49
	1.9	9.2	17.48	3.61	84.64
	2	10.5	21	4	110.25
SUM	16.5	100.4	152.59	25.85	923.58

Solutions for parts (a) to (c) are as below:

(d) Correlation coefficient was already calculated in part (c) as 0.707

(e) Using the data analysis tool in Excel, we get 90% confidence intervals for the intercept and slope as below:

Using the above, we get the following table and plot: