Business and Economic Statistics Essays

Business and Economic Statistics Essays Business and Economic Statistics Essay Business and Economic Statistics Essay ECMT1010 BUSINESS AND ECONOMIC STATISTICS A ASSIGNMENT Semester 1, 2011 This assignment is worth 10% of your total mark. It must be handed in by 4:30pm on Friday, 3 June in the marked drop-off boxes in the Merewether building (Level 2, reception area). Late assignments will not be accepted and will result in a zero mark. The assignment must be done individually and plagiarism will result in severe penalty and possibly a zero mark. The assignment will be marked out of 50. Marks for each question are shown. Data for analysis: Suppose that you are working for an environmental group on household electricity consumption. You are primarily interested in quantifying what factors could affect the household electricity consumption. The environmental group provided a data set that contained the information of 50 randomly selected households in Western Sydney. The data are recorded in an EXCEL file that you can download from the course web site. Q1a (8 marks) The leader of the environmental group suspects that homes (referred to as population 1) consume more electricity than units (referred to as population 2). Perform a hypothesis test to validate such suspicion. You must clearly state your null and alternative hypothesis, your conclusions, and the related output that lead to your conclusions. Use ? =0. 05 and assume unequal variances. Q1b (8 marks) However, the test in Q1 does not take the size of the building into considerations. So you compute the electricity consumption per week per square meter. We call this the electricity consumption rate. Perform a hypothesis to verify if the electricity consumption rate of homes is higher than that of units. You must clearly state your null and alternative hypothesis, your conclusions, and the related output that lead to your conclusions. Use ? =0. 05 and assume unequal variances. Q1c (4 marks) Based on your analysis in Q1a and Q1b, is it true that homes consume more electricity than units? Q2 (25 marks) You decide to run a simple linear regression using the electricity consumption as the dependent variable and the size of the building as the independent variable (use all 50 samples). a) Estimate the regression equation between these variables, showing all relevant estimation output, i. e. estimates, t-statistics, p-values, etc. ) State and interpret the R2 value from this regression fit and comment on the strength of the relationship. c) Examine the residuals from your regression. Are the assumptions of a simple linear regression model satisfied? (Hint: you might enlist all the related assumptions and perform related test one by one. ) d) A new home with 180 square meters is completed. Construct a 90% prediction interval of the electricity consumption per week. Q3 (5 marks) Give a summary of your conclusions about the relationship among electricity consumption, square meters, and types of building. END OF ASSIGNMENT