In a Simple Regression with an Intercept and a Single $\left( T S S = \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \bar { Y } \right) ^ { 2 } \right)$

question 18

Essay

In a simple regression with an intercept and a single explanatory variable, the variation in Y $\left( T S S = \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \bar { Y } \right) ^ { 2 } \right)$ can be decomposed into the explained sums of squares $\left( E S S = \sum _ { i = 1 } ^ { n } \left( \hat { Y } _ { i } - \bar { Y } \right) ^ { 2 } \right)$ and the sum of squared residuals $\left( \operatorname { SSR } = \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 } = \sum _ { i = 1 } ^ { n } \left( Y _ { i } - \hat { Y } \right) ^ { 2 } \right)$ (see, for example, equation (4.35)in the textbook).
Consider any regression line, positively or negatively sloped in {X,Y} space. Draw a horizontal line where, hypothetically, you consider the sample mean of Y $( = \bar { Y } )$ to be. Next add a single actual observation of Y.
In this graph, indicate where you find the following distances: the
(i)residual
(ii)actual minus the mean of Y
(iii)fitted value minus the mean of Y

Identify the conditions under which an electronic agreement becomes a binding contract.

Understand the application and limitations of the postbox rule in contract law.

Recognize the enforceability and exceptions of various forms of contracts and promises, including gratuitous promises and charitable donations.

Discern the legal significance of the quantum meruit principle in contract breaches.

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Definitions:

Firms' Costs

The expenses incurred by businesses in the production of goods or services, including labor, materials, and overhead costs.

Quantity Supplied

The extent of a good or service that merchants are willing and have the capacity to offer at a pre-determined price.

Supply Curve

A graphical representation showing the relationship between the price of a good or service and the quantity of that good or service suppliers are willing to offer for sale at various prices.

Price of Sugar

The cost at which sugar is sold or bought in the market.