How many observations about the real estate market in Ultimate City have been acquired? 

QUESTION 1

1. How many observations about the real estate market in Ultimate City have been acquired?

QUESTION 2

1. What explanatory data (independent variables) are available?

QUESTION 3

1. How many categorical variables are available?

QUESTION 4

1. Does it initially look like you will need to make any adjustments to account for differences in units of measure, e.g. from data in 1,000’s to data in 1’s?

Yes

No

QUESTION 5

1. Are any of the variables in the data highly correlated?

Yes

No

QUESTION 6

1. If you answered yes to Question 5, which variable would you consider dropping first?

		Age
		Pool
		Large lot (lgelot)
		Bedrooms
		I answered “no” to Question 5
		Baths

QUESTION 7

1. The data contain two variables that might be used as indicator variables; lot size (lgelot) and pool.

What proportion of the data is lgelot?  (leave your answer as a decimal number not percent)

QUESTION 8

1. The data contain two variables that might be used as indicator variables; lot size (lgelot) and pool.

What proportion of the data is pool?  (Leave your answer as a decimal number not percent)

QUESTION 9

1. Is the distribution of your dependent variable normal?

Yes

No

QUESTION 10

1. If you answered no to Question 8 what transformation would you probably use to help force compliance with the assumption of normality?

		ln(variable) i.e. take the natural log of the variable
		Inverse (1/variable)
		I answered “yes” to Question 8
		Square root
		Quadratic

1. Consider the different kinds of models we have studied in ANA 500, e.g. simple linear, multivariable linear, non-linear either simple or multivariable, etc.  Given the tools you have available today, which one of the following is the “test” you would use to determine which type of model is best?

		Test of Independence
		Test for Homogeneity
		The test I would use is not in this list of tests
		Comparing the sums-of-squares errors (SSE’s) to find the least error
		Goodness-of-Fit Test

QUESTION 12

1. Test different models to determine which model you should use to compute the information Ultimate Realty needs.  That is, consider the differences in the sum-of-squares-error values, frequency plots to check normality, scatter plots to check linearity, etc.  From the choices below select which model you have found is best overall.

		None of the models tested will provide results
		All the models tested will provide the same accuracy and quality of results
		Multivariable log-quadratic
		Simple log-linear (non-linear, logarithmic)
		Simple log-quadratic
		Multivariable linear
		Simple quadratic (non-linear, polynomial)
		Multivariable log-linear
		Multivariable quadratic
		Simple linear

QUESTION 13

1. As often happens, regardless of what you think is best your boss decides that you will use a multivariable log-quadratic model as follows.  Use the variables price, size (sqft), size squared (sqft_sq), age, age squared (age_sq), bedrooms, and baths.  And, he/she says for you to take the natural log of the price variable, i.e. ln(price).

 

Except for the ends of the plot, the Q-Q plot generally indicates that the assumption/condition of normality has been met.

Yes

No

QUESTION 14

1. As often happens, regardless of what you think is best your boss decides that you will use a multivariable log-quadratic model as follows.  Use the variables price, size (sqft), size squared (sqft_sq), age, age squared (age_sq), bedrooms, and baths.  And, he/she says for you to take the natural log of the price variable, i.e. ln(price).

The plot of residuals versus fits indicates that the assumption/condition of linearity has been met.

Yes

No

QUESTION 15

1. Build and use the model your boss wants to answer the following questions.

Consider the intercept and all coefficients of this model to select the best choice(s) from the list below.

		There is no way to tell anything about statistical significance from the results.
		The intercept and all coefficients are statistically significant.
		Neither the intercept nor any of the coefficients are statistically significant.
		The variable, age_sq, is not statistically significant.

QUESTION 16

1. The R-squared value indicates that very little of the variance in the data is explained by the model.

True

False

QUESTION 17

1. Hypothesis tests can be conducted using a t-statistic and/or its related P-value.  If the t-statistic falls in the rejection or the P-value is less than the level of significance of the test then the null hypothesis must be rejected.  The alternative, for example a test to establish that a relationship between an explanatory (independent) variable and a response (dependent) variable exists is accepted.

True

False

QUESTION 18

1. The boss has convinced you that this is a pretty good model for Ultimate Realty.  Because the boss is particularly interested in how size and age affects house prices evaluate those parameters and use the results to answer the following questions.

Test the coefficient of size to determine if size is related to price.  Based on a hypothesis test using the null hypothesis,  i.e. the coefficient equals zero.  There is not sufficient evidence (statistical significance) that a relationship exists between the explanatory variable and the response (dependent) variable.  Therefore, size can be removed from the regression model without any impact on the results.

True

False

QUESTION 19

1. Does the age of a house really affect its price?  Again based on a hypothesis test for this model and its variables, the coefficient of age equals zero indicating that there is no relationship between the explanatory variable, age, and the response (dependent) variable price.

True

False

QUESTION 20

1. One of Ultimate’s sales agents has just spoken with Mr. Road Runner about listing his house.  The house is 10 years old, has 2000 square feet of living area (sqft), and 3 bedrooms.  How much should Ultimate’s agent tell Mr. Road Runner he should list his house for, i.e. the price?

QUESTION 21

1. What is the upper bound for a 95% confidence interval in dollars (USD) based on the information in part d above?

QUESTION 22

1. What is the lower bound for a 95% confidence interval in dollars (USD) based on the information in part d above?

QUESTION 23

1. If Mr. Road Runner increase his living room with 200 more square feet of living space, how much would that increase the price of the house to (in dollars USD)?

QUESTION 24

1. The boss would like to look at some different results.  He/she says it is because there are two explanatory variables that have not yet been explored, large lot size (lgelot) and pool.  He/she wants you to remove the second-order terms from the model, add these variables and the variable baths to the model and generate an interaction term between large lot and size (lgelot x sqft).  This results in a model expressed as:

To answer this question, consider the coefficients in this new model.  Now, all coefficients are statistically significant.

True

False

QUESTION 25

1. How much more, in a percentage, is the price of a house on a large lot (greater than 0.5 acres) than a house on a small lot?

QUESTION 26

1. What is the percent increase in price for an additional 100 square feet of living space if the house is NOT on a large lot (holding all other variables constant)?

QUESTION 27

1. What is the percent increase in price for an additional 100 square feet of living space if the house is on a large lot?