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# Foundation Skills in Data Analysis MIS770A ## Question 1a

To determine relationship between House Price and Suburb, the contingency tables (also called cross tabulation is constructed. For the given dataset including house price and suburb, the contingency table is constructed (See: Excel). From the contingency table, it can be depicted that there is no significant relationship between house price and suburb (Weiers, 2010). It is because there is no increasing or decreasing pattern in the house prices along with the suburbs. Houses with different prices are present in different suburbs.

### Question 1b

To determine linear or non-linear relationships of the independent variables with House Price, scatter diagrams showing trendline and R2 are constructed. The scatter diagram shows that there is a positive relationship between house price and land size (See: Excel). The data points in plot appear to be randomly distributed as they are not close to the line (Groebner et al., 2011). Apart from this, in the scatter diagram between house price and house area, it can be determined that shows that there is a positive relationship between both variables as R square is 0.317 but it is not a strong relationship (See: Excel). It is because the data points in plot appear to be randomly distributed as they are not close to the line. In addition, the scatter diagram also shows that house price and weekly rent show a positive and weak relationship (See: Excel).

### Question 1c

Correlation coefficient (R) shows the strength of the relationship between variables (Newbold et al., 2012). It is determined by using formula SQRT R2 and R2 was determined by the regression line on scatter diagram through trendline function in excel.

House Price vs LandSizeSqm:

R2: 0.175 (determined on scatter diagram through regression equation and trend line)

R: SQRT R2 =SQRT 0.175 = 0.418

House Price vs HouseAreaSqm:

R2: 0.317(determined on scatter diagram through regression equation and trend line)

R: SQRT R2 =SQRT 0.317= 0.563

House Price vs WeeklyRent:

R2: 0.432(determined on scatter diagram through regression equation and trend line)

R: SQRT R2 =SQRT 0.432 = 0.657

From the correlation table, it can be determined that weekly rent as independent variable has the strongest relationship with house price as the value of correlation coefficient is the highest for weekly rent (0.657) (See: Excel).

### Question 2 a

On conducting regression on excel by considering two variables house price (dependent) and house area (independent), regression model is obtained (See: Excel). From this regression model, it can be determined that m= 1.9537 and c= 367.4176 (See: Excel)

 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 367.4176 74.2445 4.9488 0.0000 220.3933 514.4419 HouseAreaSqm 1.9537 0.2637 7.4077 0.0000 1.4314 2.4760

m: slope that is obtained from regression model as coefficients in x value(house area)

c: constant value obtained from regression model as intercept

Regression equation can be presented as below:

y= mx+c

So,

House price= 1.9537* House Area + 367.4176

= 1.9537*500+367.4176

=\$1344.27

#### Question 2b

Based on the correlation matrix, it can be stated that house prices are positively correlated with independent variables including land size, house area and weekly rent. It was determined by using correlation function on excel and calculated correlation between each variables. From this it can be determined that the correlation between house price and land size is 0.4193, while the correlation between house prices and house area is 0.5634 and correlation between house price and weekly rent is 0.6577. It shows that all correlations are positive indicating a strong correlation between house price and other variables. From this regression model (showing from slope values in regression), it can be determined that if land size is changed by 1 sqm then the price of house will change by \$0.2494. If house area is changed by 1 sqm then the house price will change by \$0.9241. If the weekly rent changes by \$1 then the house price will change by \$0.6289. For all dependent variables, p- value is approx zero or less than 0.05 so it can be depicted that the relationship between house price and other dependent variables is statistically significant.

The R-squared is used to measure how well the model fits the data so well. It further demonstrates how data is so close to the fitted regression line. If the R-squared is 0% then there is no variability of data around mean. If it is close to 100%, then the model explains the variability of data around mean. By conducting multiple regression model with consideration of house price as dependent variable (Y) and other variables as independent variables (X), it can be discussed that  R2 value is 0.5586 indicating model explains 55.86% variability of the response data around its mean. It also implies the model fits data in better way (Groebner et al., 2011).

#### Question 3a

To describe the trend in Melbourne house prices, the scatter diagram is plotted by considering the median price of established house transfers in Melbourne in different periods between year 2002 and 2016 (See: Excel). From the scatter diagram, it can be determined that there is an increasing trend in the median price of established house transfers in Melbourne in different periods between year 2002 and 2016. Median price of established house transfers is increasing consistently in quarter of each year from 2002 to 2012. It shows the positive trend in these prices over the periods (Gibbons and Chakraborti, 2011). In year 2002, there is an increasing trend in house price over the quarters as it increased from \$241000 to \$280000. At the same time, in year 2003, there is also an increasing trend in house price, but it declined in first quarter of year 2004. There were fluctuations in house prices in each quarter of year 2004 followed by a decline in first quarter of year 2005. In year 2005, there was an increasing trend in house price as it increased from \$310000 to \$320000 with no change in second and third quarter. In first quarter of year 2006, the house prices slightly declined from fourth quarter of 2005 but after this it increased till fourth quarter of year 2006. a decline was noticed in first quarter of 2007 but after this it increased till fourth quarter of the same year. In year 2008, a decline was noticed in first quarter with increase in second quarter and then decline in third quarter with no change in fourth quarter. In year 2009, first quarter showed the decline in house price as compared to previous year but it increased in next quarters. First quarter in year 2010 also showed decline in house prices but next quarter showed an increase with a decline in third quarter. In year 2011, a decline was noticed in first quarter with an increase in second quarter followed by a decline in next quarters. In year 2012, first quarter showed decline in house prices with overall an increase in next quarters with slight decline in third quarter. In year 2013, house prices in first quarter also declined but these prices increased in next quarters consistently. The same pattern was noticed again as the first quarter showed decline in house prices in year 2014 but it increased in next quarters with a decline in third quarter. In year 2015, a decrease in house price was noticed with increasing trend in remaining quarters. However, in year 2016, first quarter showed again a decline but remaining quarters showed the increasing trend with slight decrease in third quarter.

### Question 3b

In order to forecast the house prices for the all quarters in year 2017, the regression equation was used that was obtained from the scatter diagram and drawing a trend line from the trendline function on excel. From the regression line it was determined that the regression equation is as below:

y=6.327x+237.4 (See: Excel)

Quarter 1 2017 (period 61):

y= 6.327x+237.4

= 6.327*61+237.4

= 623.4 (\$,000)

=\$623,400

Quarter 2 2017 (period 62):

y= 6.327x+237.4

= 6.327*62+237.4

= 629.7 (\$,000)

=\$629,700

Quarter 3 2017 (period 63):

y= 6.327x+237.4

= 6.327*63 +237.4

= 636 (\$,000)

=\$636,000

Quarter 4 2017 (period 64):

y= 6.327x+237.4

= 6.327*64+237.4

= 642.4 (\$,000)

=\$642,400

On comparing house prices in year 2016, it can be determined that the house prices will decrease in year 2017 as compared to year 2016. In first quarter of 2017, the house price will decline as same pattern in previous years, but after this, it will increase in each quarter of 2017. Overall prices in year 2016 will be lower than the fourth quarter of year 2016.

#### References

Gibbons, J. D., and Chakraborti, S. (2011). Nonparametric statistical inference. In International encyclopedia of statistical science (pp. 977-979). Springer Berlin Heidelberg.

Groebner, D.F., Shannon, P.W., Fry, P.C. and Smith, K.D., (2011). Business statistics: A decision making approach. UK: Prentice Hall/Pearson.

Newbold, P., Carlson, W., & Thorne, B. (2012). Statistics for business and economics. Pearson.

Weiers, R. M. (2010). Introduction to business statistics. Cengage Learning. 