In the BLUE property of OLS slope, the best estimator means thata.If one computes the standard error of the regression slope, then it shall be less than the standard error of the slope had we used some other formula for slopeb.If one computes the value of the regression slope, then it shall be less than the slope had we used some other formula for slopeClear my choice
Question
In the BLUE property of OLS slope, the best estimator means thata.If one computes the standard error of the regression slope, then it shall be less than the standard error of the slope had we used some other formula for slopeb.If one computes the value of the regression slope, then it shall be less than the slope had we used some other formula for slopeClear my choice
Solution
The BLUE property of OLS (Ordinary Least Squares) refers to the "Best Linear Unbiased Estimator". In the context of OLS, "best" refers to the estimator having the smallest variance among all unbiased estimators.
a. The statement is correct. The "best" in BLUE refers to the estimator that has the smallest variance. In other words, if we compute the standard error (which is the square root of the variance) of the regression slope, it should be less than the standard error of the slope had we used some other formula for the slope. This is because the OLS estimator minimizes the sum of the squared residuals, thereby giving us the smallest possible variance.
b. The statement is incorrect. The "best" in BLUE does not refer to the size of the slope coefficient itself. Instead, it refers to the precision of the estimator. The OLS estimator gives us the line of best fit through our data, but it does not necessarily mean that the slope of this line will be smaller than if we used a different formula for the slope. The value of the slope depends on the relationship between the variables, not on the estimation method.
Similar Questions
In a simple regression analysis, the slope represents:A.The estimated value of the dependent variable (Y) when X is zero.B.The point where the regression line intersects the Y-axis.C.The strength of the linear relationship between X and Y.D.The expected change in the dependent variable (Y) for a one-unit change in the independent variable (X).
The slope of a regression line represents:a.The average change in the dependent variable for a unit change in the independent variableb.The intercept of the regression linec.The correlation coefficient between the variablesd.The residual value in regression analysis
Which of the following is the correct interpretation of the slope of the regression line?A student who performs 1 point better than another on the upper-level course is likely to perform 1 point worse in the introductory course.A student who performs 1 point worse than another on the upper-level course is likely to perform 1 point better in the introductory course.A student who performs 1 point better than another in the introductory course is likely to perform 10 − 1.4 = 8.6 points better in the upper-level course.A student who performs 1 point better than another on the introductory course is likely to perform 1 point better in the upper-level course.
A local real estate valuer wants to develop a statistical model to predict the value of properties in a certain suburb. One of the many variables thought to be an important predictor of real estate value is the floor area of the house. Let y = value of the property (in $) and x = floor area of the house (in square metres). Using data collected for a sample of n = 82 properties, the valuer created the following linear regression model:𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑣𝑎𝑙𝑢𝑒^=196,600+2,185∗𝐹𝑙𝑜𝑜𝑟 𝑎𝑟𝑒𝑎Interpret the estimate of the slope of the line.Hint: The "slope" of a line and how to interpret it is first referenced in the Section 2.6 notes.Question 3Select one:When the floor area of a house is zero square metres (section only), I predict the property value to be $2,185.For each additional one square metre of floor area in the house, I predict the property value to increase by $2,185For each additional dollar of property value, I predict the floor area in the house to increase by 2,185 square metres.For a property with zero square metres of floor area in the house (section only), I predict the propoerty value to be $196,600.For each additional one square metre of floor area in the house, I predict the property value to increase by $196,600.Clear my choice
How is the slope of the line of best fit calculated using the least squares method?Select one:a.By dividing the sum of the y values by the sum of the x valuesb.By dividing the sum of the product of the x values and the y values by the sum of the squares of the x valuesc.By dividing the sum of the product of the x values and the y values by the sum of the x valuesd.By dividing the sum of the y values by the sum of the squares of the x values
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