Statistical models can provide a cheap and quick way to describe a real world situation.
Give two other reasons why statistical models are used.
A scientist wants to develop a model to describe the relationship between the average daily temperature, \(x ^ { \circ } \mathrm { C }\), and her household's daily energy consumption, \(y \mathrm { kWh }\), in winter.
A random sample of the average daily temperature and her household's daily energy consumption are taken from 10 winter days and shown in the table.
\(x\)
- 0.4
- 0.2
0.3
0.8
1.1
1.4
1.8
2.1
2.5
2.6
\(y\)
28
30
26
25
26
27
26
24
22
21
$$\text { [You may use } \sum x ^ { 2 } = 24.76 \quad \sum y = 255 \quad \sum x y = 283.8 \quad \mathrm {~S} _ { x x } = 10.36 \text { ] }$$
Find \(\mathrm { S } _ { x y }\) for these data.
Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + b x\)
Give the value of \(a\) and the value of \(b\) to 3 significant figures.
Give an interpretation of the value of \(a\)
Estimate her household's daily energy consumption when the average daily temperature is \(2 ^ { \circ } \mathrm { C }\)
The scientist wants to use the linear regression model to predict her household's energy consumption in the summer.
Discuss the reliability of using this model to predict her household's energy consumption in the summer.