Use Computer Software to Find the Best Multiple Regression Equation $X _ { 1 } , X _ { 2 } , X _ { 3 }$

question 19

Multiple Choice

Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, $X _ { 1 } , X _ { 2 } , X _ { 3 }$ $$\begin{array} { | c c c c | } \hline Y & X & X & \\15 & 1.2 & 16 & \\15 & 1.2 & 16 & \text { CORRELATION COEFFICIENT } \\17 & 1.0 & 16 & Y / X _ { 1 } = 0.886 \\6 & 0.8 & 9 & Y / X _ { 2 } = 0.965 \\1 & 0.1 & 1 & \\8 & 0.8 & 8 & Y / X _ { 2 } = 0.932 \\10 & 0.8 & 10 & Y / X _ { 2 } , X _ { 1 } = 0.943 \\17 & 1.0 & 16 & \\15 & 1.2 & 15 & \text { COEFFICIENTS OF DETERMINATION } \\11 & 0.7 & 9 & \\18 & 1.4 & 18 & \\16 & 1.0 & 15 & \\10 & 0.8 & 9 & \\7 & 0.5 & 5 & \\18 & 1.1 & 16 & \\\hline\end{array}$$

• A) \(\hat { Y } = 1.38 - 5.53 X _ { 1 } + 1.33 X _ { 2 }\)
• B) \(\hat { Y } = - 0.49 + 14.07 X _ { 1 }\)
• C) \(\hat { Y } = 1.25 - 1.55 X _ { 1 } + 5.79 X _ { 2 }\)
• D) \(\hat { Y } = 0.42 + 0.99 X _ { 2 }\)

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Definitions:

Sales Forecast

The process of estimating future sales. Accurate sales forecasts enable companies to make informed business decisions and predict short-term and long-term performance.

Holt-Winters Additive Model

A forecasting technique that captures seasonality, trend, and level in time series data, adding them together for prediction.

Exponential Smoothing

It is a rule of thumb technique for smoothing time series data using the exponential window function.

Additive Model

A statistical model where the effect of variables is linear and additive, assuming each variable contributes a separate and additive amount to the final outcome.