Which of the Following Statements Are Not True?
A) the Slope

question 99

Multiple Choice

Which of the following statements are not true?

• A) The slope \(\hat { \beta } _ { 1 }\)
• Of the least squares line is an unbiased estimator of the slope coefficient \(\beta _ { 1 }\)
• Of the true regression line.
• B) The variance \(\hat { \beta } _ { 1 }\)
• Of the least squares line equals the variance \(\sigma ^ { 2 }\)
• Of the random error \( \varepsilon\)
• Divided by \(\sqrt { S _ { xx } }\)
• , where \(S _ {xx } = \sum \left( x _ { i } - \bar { x } \right) ^ { 2 }\)
• C) Values of \(x _ { i}\)
• All close to one another imply a highly variable estimator \(\hat { \beta } _ { 1 }\)
• Of the slope \(\beta _ { 1 }\)
• Of the true regression line.
• D) Values of \(x _ { i }\)
• That are quite spread out results in a more precise estimator \(\hat { \beta } _ { 1 }\)
• Of the slope \(\beta _ { 1 }\)
• Of the true regression line
• E) All of the above statements are true

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Definitions:

Engel Curve

A graphical representation showing how household spending on a particular good or service changes with income.

Upward-Sloping

A description of a line or curve on a graph that indicates an increase in a variable as another variable increases.

Individual Demand Curve

Curve relating the quantity of a good that a single consumer will buy to its price.

Price-Consumption

Illustrates how a consumer's optimal consumption bundle changes in response to changes in the price of a good, holding all else constant.