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

question 166

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 Income in the regression model?

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

Connective Tissue

Bodily tissue whose function is to uphold, link, or demarcate distinct tissues and organs.

Less Elastic

Referring to materials or tissues that have a decreased ability to resume their normal shape after being stretched or compressed.

Older Adults

Individuals in a later stage of life, often categorized as being aged 65 years and older, experiencing various physiological and social changes.

Elongated Fibers

Refers to cells that are significantly longer than they are wide, often found in muscle and connective tissues.