Discussion on Use the estimate, constructed in Question 1, for the population proportion of residential properties for sale which are units, to address your relative’s concern that their choice will be limited if they restrict their search to units.

All the quantitative data is arranged in the form of the table under the relevant headings of "price", number of bedrooms, number of bathrooms, and type of residential option. According to the case scenario, relative is interested to purchase the property under the identified budget. Therefore, only selecting units from the available property options rather than including houses will limit the search options. In the available data, only 37 property options fall in the category of unit. While the rest of all relates to the category of the house. Somehow, to test this scenario two hypotheses are developed which will be used in the statistical testing process and population proportion analysis. Thus, the analysis and testing suggest that the hypothesis is true and the chances of error in testing are low. Conclusively, it can be said that by creating a restriction of units search will be limited for relative.  

Question 2

100 to 200 words and 0.5 to 1 page

Use your answer to Question 2:

In the location specified by your sample, is the mean two and three bedroom residential property price more than $330,000?

to answer your relative’s question. That is, is the location too expensive?

The mean price for all available options regarding the property such as units and houses is around $306,435 by including all options for houses and units. The average is calculated by adding up all prices and then dividing the answer by the total number of options.

Somehow, the mean price of units is around 285, 916 (or 278 thousand). However, the mean price for the houses is almost $340,995. See the following table (in appendix) for calculated mean values for available property types in the selected locality.

In the presented table (see appendix), the specific mean prices represent the average price demanded by the property owners offering 2 to 3 bedrooms in units or houses of the selected locality. Total available option regarding this specification is a total of 69 out of the 100 collected property options. Considering these values for testing expensiveness it can be said that average prices for houses are greater than units. Thus, calculation suggests that houses are expensive as compared to units. Projecting on results, the locality is really expensive.

Question 3

100 to 200 words and 0.5 to 1 page

Use your estimate for the mean difference in price between units and houses for sale in the location specified by your sample, constructed in Question 3, to answer your relative’s question. That is, how much they would save if they purchased a unit instead of a house.

The estimate and statistical analysis represent a huge difference in price between houses and units for sale in the specified location by the relative. Considering the calculation of mean prices for the 2 and 3 bedroom property option (including both houses and units) is greater than the maximum budget of the relative. According to the case scenario, the relative has a total budget of $330, 000 in which he is interested to purchase a house or unit with 2 to 3 bedrooms.  

The amount of $330,000 is greater than the mean prices for the property with required features (regarding a total number of rooms). Total 69 properties are having 2 and 3 bedrooms and the average prices for these property options is around $306,435. The total difference between the average price of these properties and budget is limited to $23,565. Although, the difference between the average price of units and the budget is $44,084. Somehow, the average price of houses is greater than the maximum budget as the difference in prices is around $10,995. Thus, if they purchase unit they would save $44,084.

Questions 4 and 5

100 to 300 words and 0.5 to 2 pages

Use the simple and multiple linear regression models developed in Questions 4 and 5 to provide, and justify, a linear model to predict price from several bedrooms and/or number of bathrooms and/or type (house or unit)

·         Include and justify the simple or multiple linear regression model which best fits the data.

·         Discuss and interpret the values of the regression coefficients and coefficient of determination of the best model.

·         Present the results without unnecessary statistical jargon.

Predict price from several bedrooms and/or the number of bathrooms and/or type (house or unit) varies from each other but have a similar trend therefore based on the historical information we can predict the future prices. The multiple linear regression calculated regression and variance in the values based on which further predictions are made. The p-value represents the significance value for hypothesis testing. Somehow, the statistical analysis recommends that an increase in the total number of rooms would also increase prices for the houses and units. See the following best fit line graph inclining towards maximum prices required to have more bedrooms in the property.

Appendices for Part B -

Appendix B.1 – Statistical answer for Question 1

Considering this now calculating that:

Confidence Intervals for Population Proportion

Upper Bound and Lower Bound of Normal distribution.

Appendix B.2 – Statistical answer for Question 2   

Appendix B.3 Statistical answer for Question 3

Appendix B.4 Statistical answers for Questions 4 and 5

Assumptions and Variables Defined

Question 4 Simple Linear Regression Model

The simple linear regression model only includes two variables: one independent and second dependent variable. Simple linear regression only represents a linear relationship or non-linear trend between quantitative data for research variables. In the linear regression model, regression coefficients are determined by considering the specification of research variables.

Question 5 Multiple Linear Regression Model

In this calculation, the independent variables are the total number of bedrooms, the total number of bathrooms, and house types. Somehow, dependent variables are prices for the units and houses in the selected area. The regression analysis is used to test a hypothesis about the impact of independent variables on the dependent variable (prices of units and houses). The greater values of coefficient indicate a strong relationship between prices and independent variables (total number of bedrooms, the total number of bathrooms, and house types).