Instruction 13 ANOVA Note: Adj R Square = Adjusted R Square; Std

question 229

Multiple Choice

Instruction 13.30
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) , family size (Size) and education of the head of household (School) . House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:
OUTPUT
SUMMARY
Regression Statistics
$\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adj. R Square } & 0.726 \\ \text { Std. Error } & 5.195 \\ \text { Observations } & 50 \end{array}$

ANOVA
$\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 & \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 & \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 & \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error
-Referring to Instruction 13.30,at the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of School in the regression model?

• A) School is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
• B) School is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
• C) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
• D) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.

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Definitions:

Bayesian Statistics

A statistical method that applies probability to statistical problems, focusing on the posterior distribution of parameters by incorporating prior knowledge.

Probability Distributions

Mathematical functions that provide the probabilities of occurrence of different possible outcomes for an experiment.

Expected Value

A calculated average of all possible values in a random variable, weighted by each value's probability of occurrence.

Perfect Information

A situation in which all participants have access to all relevant information without any restrictions.