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

question 146

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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
 Multiple R 0.865 R Square 0.748 Adj. R Square 0.726 Std. Error 5.195 Observations 50\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
df SS  MS F Signiff  Regression 3605.7736901.44340.0001 Residual 1214.226426.9828 Total 494820.0000 Coeff  StdError t Stat p value  Intercept 1.63355.80780.2810.7798 Income 0.44850.11373.95450.0003 Size 4.26150.80625.2860.0001 School 0.65170.43191.5090.1383\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,suppose the builder wants to test whether the coefficient on Income is significantly different from 0.What is the value of the relevant t-statistic?

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Definitions:

Preferred Shares

Preferred Shares are a type of stock that grant holders preferential treatment over common stockholders in terms of dividends and assets during liquidation, but usually do not carry voting rights.

Rate of Return

The increase or decrease in the value of an investment, shown as a percentage of the original amount invested, over a given timeframe.

Floatation Costs

Flotation costs are the expenses incurred by a company in issuing new securities, including fees and commissions paid to underwriters, legal fees, and registration fees.

After-Tax Cost of Debt

This refers to the net cost of debt considering the effect of taxes, representing the actual financial cost of debt to a company after tax deductions.

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