Buss1020 Assignment

BUSS1020 Group Assignment

Question 1:

1. [pic 1]

Let the average electricity used by homes be µ1, by units, µ2:

H₀: µ₁ ≤ µ₁

H₁: µ₁ > µ₂

n₁ = n₂ =25 < 30, therefore CLT does not apply, assume sampling distribution is approximately normal. Also assume sample is randomly selected.

α = 0.05, σ₁, σ₂ are unknown, therefore use S₁, S₂, to estimate, therefore upper tail t-test with unequal population variances.

[pic 2]

[pic 3]

[pic 4]

[pic 5]

[pic 6]

Therefore, reject H₀ at 5% level of significance

There is sufficient evidence to say home consume more electricity than units at a 95% level of confidence.

1.  [pic 7]
2. Let the average electricity used by homes be µ1, by units, µ2:

H₀: µ₁ ≤ µ₁

H₁: µ₁ > µ₂

n₁ = n₂ =25 < 30, therefore CLT does not apply, assume sampling distribution is approximately normal. Also assume sample is randomly collected.

α = 0.05, σ₁, σ₂ are unknown, therefore use S₁, S₂, to estimate, therefore upper tail t-test with unequal population variances.

[pic 8]

[pic 9]

[pic 10]

[pic 11]

[pic 12]

Therefore, do not reject null hypothesis at 95% significance.

There is insufficient evidence to conclude that home consume more electricity than units at a 95% level of confidence.

1. It is partly true. It can be concluded that the population of homes consume more electricity than the population units at 95% confidence.

But if the size of each building is acknowledged as a dependent variable, it cannot be concluded that population of homes consume more electricity per square metre, that is, have a higher electricity consumption rate than units. This is because the null hypothesis in 1b), that the electricity consumption rate of houses was less than or equal to the electricity consumption rate of units, was not rejected.

Question 2:

1. [pic 13]

Regression is used to predict the value of a dependent variable based on the value of at least one independent variable. This will explain the impact of changes in an independent variable on the dependent variable.

Simple linear regression equation:

[pic 14]

Interpretation of b₀ (0.5350) when the size of the building is 0, the electricity consumption is 0.5350. However, this makes no intuitive sense as the size of the building cannot be zero.

Interpretation of b₁ (1.0818) For every one-unit increase in the size of the building, on average, the mean value of the electricity consumption increases by 1.0818.

The standard error of estimate 13.1224. This is the variation about the prediction line.

[pic 15]

As r squared is close to 1, there is a strong linear relationship between electricity consumption (dependent variable) and the size of the building (independent variable). 91%, of the variation of the electricity consumption is explained by variation in the size of the building. The remaining 9% of the variation is unexplained and due to factors outside of the regression model such as the number of people living in each house/unit etc.

1. [pic 16]

Residual:[pic 17]

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There does not seem to be any observable pattern; the residuals seem to be randomly spread out. The assumptions of regression do not appear to be seriously violated.

The assumptions of a simple linear regression model:

LINEARITY

Whilst there is widespread scatter in the residual plot, there appears to be no clear pattern or linear relationship between the residuals and Xi (the size). The residuals seem to be evenly spread above and below 0 for different values of X. Therefore the linear model remains appropriate for the data.