4. Identify and justify the shapes of the distribution for house price ($000) and lot size (m2) through graphical techniques. Conduct descriptive summary statistics using Excel Data Analysis for those two variables. Calculate first quartile, third quartile and interquartile range. Report on shapes, central tendency and spread of these two variables. 5. The market research manager believes the average Sydney house price should be different from $835,000. Test at 5% level of significance to assess whether the manager’s claim is true. Calculate the 95% confidence interval for true mean and interpret the resulting bound. 6. The market researcher would like to compare Sydney house prices ($000) in two different types of houses, one having a recreational room and the other without a recreational room. Assuming that the population variances for both type of house prices are equal, perform an appropriate hypothesis test, at 95% confidence. The market researcher is interested in determining whether there is a significant difference in the average house prices in two different types of houses. Find 95% confidence interval for the difference in means and interpret the resulting bound. 7. Draw a scatter diagram with lot size of a property in square metres (m2) as the x-axis and price of a house in thousand dollars as the y-axis. Briefly describe the scatter diagram. Determine the least square regression line. Interpret the slope and the vertical intercept coefficients. Perform a hypothesis test, at the 5% significance level, to determine if there is a relationship between lot size of a property and price of a house. Provide the lower and upper limits of the 95% confidence interval for the slope. Predict the estimated house price with a lot size of a property in square metres (m2) of 585. 8. Develop a regression model to predict the house price, based on lot size, number of bedrooms, number of full bathrooms, storeys, driveway, recreation, gas heat, aircon and garage. • State the predicted multiple regression equation. • Interpret the regression coefficients. • Perform a residual analysis for the house price data. Evaluate whether the assumptions of regression have been seriously violated. • Is there a significant relationship between house price and the 9 independent variables at the 0.05 level of significance? • At the 0.05 level of significance, determine whether each independent variable contributes to the regression model. • Indicate the most appropriate regression model for this set of data. 9. It is essential that you clearly and effectively communicate your professional writing skills though the report format and correct use of presentation and grammar. Students must include a cover page, executive summary, a table of contents, introduction, appropriate headings, and subheadings for the body of the report, conclusion, and the end reference list. Students may want to include an Appendix; however, this is not compulsory. Cover page, executive summary, table of contents and references are not included in word count.