Interpret the Slope and the Y-Intercept of the Least-Squares Regression $\hat { y } = \beta _ { 0 } + \beta _ { 1 } x$

question 25

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, $\hat { y } = \beta _ { 0 } + \beta _ { 1 } x$ , where $y =$ appraised value of the house (in \$thousands) and $x =$ number of rooms. Using data collected for a sample of $n = 74$ houses in East Meadow, the following results were obtained:
$$\begin{array} { l } \hat { y } = 74.80 + 22.75 x \\\mathrm {~s} \beta = 71.24 , t = 1.05 \text { (for testing } \beta _ { 0 } \text { ) } \\\mathrm { s } \beta = 2.63 , \mathrm { t } = 7.49 \text { (for testing } \beta _ { 1 } \text { ) } \\\mathrm { SSE } = 60,775 , \mathrm { MSE } = 841 , \mathrm {~s} = 29 , \mathrm { r } ^ { 2 } = .44\end{array}$$
Range of the x-values: $5 - 11$
Range of the $y$ -values: $160 - 300$
Give a practical interpretation of the estimate of the slope of the least squares line.

• A) For each additional room in the house, we estimate the appraised value to increase \(\$ 22,750\).
• B) For each additional room in the house, we estimate the appraised value to increase \(\$ 74,800\).
• C) For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by \(22.75\) rooms.
• D) For a house with 0 rooms, we estimate the appraised value to be \(\$ 74,800\).

Understand the factors affecting bond yields and prices, including default risk premiums, liquidity premiums, and interest rate risks.

Identify and analyze the components of an investor’s return on bonds.

Assess the influence of bond terms and market conditions on bond investment outcomes.

Understand the calculation and significance of different types of yields, including nominal yield and effective yield.

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Definitions:

Different Performance

Fulfillment of contractual obligations in a manner that is different from what was specifically agreed upon, sometimes acceptable with mutual consent.

Original Duty

The fundamental obligation or responsibility that a party has in a contractual or legal relationship.

Enforce

To compel obedience or compliance through legal or authoritative means; to ensure the fulfillment of a requirement.

Give Consideration

In contract law, the act of offering something of value, required by both parties for a contract to be legally binding.