Question 2 Simple Linear Regression Model Topic 8

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Question 1 Statistical Inference Topic 7 (10 marks)

Capital city fuel prices are often less than elsewhere in the state.

Oz-Fuel-Watch wishes to know if on the day and in the state specified by your sample the mean price of your fuel, Unleaded 91 or Diesel, was less in the capital city than elsewhere in the state.

To enable you to provide this information use Location (second column of your data) and either Unleaded 91 (third column of your data) or Diesel (fourth column of your data) with an appropriate statistical inference technique to answer the following question

On the specified day was the mean price of your fuel less in the capital city than elsewhere in the state specified by your sample?

 

Questions 2 and 3 Simple and Multiple Linear Regression (21 marks)

Oz-Fuel-Watch is interested in exploring the relationship between Unleaded 91 and Diesel prices.

You are asked to construct a model of this relationship. To do this, first develop a simple linear regression model between Unleaded 91 and Diesel prices. Then develop a multiple linear regression model with location as a second independent variable. Finally choose and interpret the linear model that best fits your data.

 

Question 2 Simple Linear Regression Model Topic 8

To explore the relationship between Unleaded 91 and Diesel prices, use your fuel (Unleaded 91/Diesel) as the independent variable and the remaining fuel (Diesel/Unleaded 91) as the dependent variable.

Using this data develop and then explore a simple linear relationship between the two variables by:

·        
Plotting the data with a scatter plot.

·        
Calculating the least squares regression equation, correlation coefficient and coefficient of determination.

·        
Interpreting the gradient and vertical intercept of the simple linear regression equation.

·        
Interpreting the correlation coefficient and coefficient of determination. Are these values consistent with your scatter plot?

 

Question 3 Multiple Linear Regression Model Topic 9

To explore if location influences the relationship between Unleaded 91 and Diesel prices add Location (second column of your data) as a second independent variable to your simple linear regression model developed in Question 2