1a

Consider

This can be re-written as

From the table

But

Hence

This can be done for .

However to obtain the value of

Mean value of

is the margin of error

Taking critical value to be then

Therefore,

.

**1b**

Substituting the parameter values in the equation

Lets assume , then

**2a (i) **

Figure 1: Box plot of outdoor temperatures

Figure 2: Box plot of average wind speed

Figure 3: Box plot of kWH

(ii)

The higher the outdoor temperature, the higher the average wind speed and the lower electricity use. This is related since during the higher temperatures more energy is needed to cool the surrounding residence. However, higher wind speed aides in cooling the residence, hence higher energy will not be needed to cool the residence as the temperatures are lowered by wind. This leads to low energy consumed in terms of electricity use. Therefore, as the wind speed and temperature increases, electricity use reduces.

**2b** (i)

Where is day of the week, is hour of the day, is the dependent variable, are coefficients

Confirm if all is going on as needed.

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