An economist estimates the following model: y = β0 + β1x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x* = x - 2. A portion of the regression results is shown in the accompanying table. ![An economist estimates the following model: y = β<sub>0</sub> + β<sub>1</sub>x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x<sup>*</sup> = x - 2. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is a 95% prediction interval for y when x equals 2? (Note that t<sub>0.025,10</sub> = 2.228.) A) [0.41, 4.63] B) [14.21, 35.35] C) [18.63, 30.93] D) [20.35, 25.65]](https://d2lvgg3v3hfg70.cloudfront.net/TB6618/11ea8309_a972_5cda_b223_9d16a2a93faa_TB6618_00.jpg)
![An economist estimates the following model: y = β<sub>0</sub> + β<sub>1</sub>x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x<sup>*</sup> = x - 2. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is a 95% prediction interval for y when x equals 2? (Note that t<sub>0.025,10</sub> = 2.228.) A) [0.41, 4.63] B) [14.21, 35.35] C) [18.63, 30.93] D) [20.35, 25.65]](https://d2lvgg3v3hfg70.cloudfront.net/TB6618/11ea8309_a972_5cdb_b223_f9fa909e5d12_TB6618_00.jpg)
According to the modified model, which of the following is a 95% prediction interval for y when x equals 2? (Note that t0.025,10 = 2.228.)
Definitions:
Interest Rate
The percentage charged or earned on an amount of money over a period, generally expressed annually.
Loan Proceeds
The amount of money provided to a borrower by a lender, typically for a specific purpose or project, which the borrower is obligated to repay under agreed terms.
Compounded Quarterly
A method where interest earned is calculated and added to the principal amount every quarter, leading to interest on interest.
Future Value
The value of an investment at a specified future date, based on an assumed rate of growth over time.
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