1. The response variable is "Price" expressed in US dollars. Use = 0.10 for significance tests. [10+5+7+8 points]

a. Using numerical and/or graphical summaries, describe the distribution of each quantitative variable. Identify if there are any outliers on dependent variable by plotting the histogram.

b. Using numerical and/or graphical summaries, describe the relationship between each pair of numerical variables.

c. Consider fitting a simple linear model using Size as the only independent variable. Provide your fitted model using Excel and interpret your regression coefficients.

d. Based on regression results in part d, conduct t-test whether there is a significant relationship between Price and independent variable. State your hypothesis, test results and conclusions.

2. Consider a multiple linear model using Size, District, and Condition as independent variables. The response variable is Price. Use = 0.05 for significance tests. Use Sergeli and Poor as the reference groups when creating dummy variables. [8+ 4 + 4 + 7 + 7 points]

a. Provide your fitted model using Excel.

b. Check for Normality and Multicollinearity based on diagnostic tools. Provide your interpretations.

c. Based on regression results in part a, write down the fitted linear models for each District and provide interpretations.

Chilanzar Sergeli

Mirabad

Yunusabad

d. Conduct a test (tests) for overall significance of the model in part a. State the hypotheses, test results and conclusions.

e. Conduct a test for significance of Size. State the hypotheses, test results and conclusions.

3. There is a perception among home buyers that an apartment with a structure of masonry is more expensive than that an apartment with concrete structure. Conduct an appropriate test whether there is statistically significant evidence for this perception. Use a = 0.05. Assume the prices of apartments in Tashkent have normal distribution and their variances are equal.

Provide your hypotheses, test results and conclusions.

4. Conduct an appropriate test to see whether condition of the apartment has any significant impact

on the price. Use a = 0.01. Provide your hypotheses, test results and conclusions.