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

question 13

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, $X _ { 1 } , X _ { 2 } , X _ { 3 }$ $\begin{array} { c c c c l } Y & X _ { 1 } & X _ { 2 } & X _ { 3 } & \\ 456 & 9896 & 29.1 & 1 & \\ 421 & 9680 & 42.3 & 2 & \\ 653 & 10449 & 29.8 & 3 & \\ 573 & 10811 & 26.0 & 4 & \text { CORRELATION COEFFICIENTS } \\ 546 & 10014 & 34.3 & 5 & \\ 499 & 10293 & 22.7 & 6 & Y / X _ { 1 } = 0.509 \\ 504 & 9413 & 24.2 & 7 & Y / X _ { 2 } = 0.280 \\ 611 & 9860 & 31.6 & 8 & \text { Y/ } X _ { 3 } = 0.930 \\ 646 & 9782 & 25.6 & 9 & \\ 789 & 12139 & 37.9 & 10 & \text { COEFFICIENTS OF DETERMINATION } \\ 773 & 12166 & 33.9 & 11 & \\ 753 & 9976 & 37.4 & 12 & \text { Y/ } X _ { 1 } = 0.259 \\ 852 & 10645 & 27.0 & 13 & \text { YI } X _ { 2 } = 0.079 \\ 755 & 9738 & 31.5 & 14 & Y / X _ { 3 } = 0.864 \\ 815 & 9933 & 39.9 & 15 & \text { Y/ } X _ { 1 } , X _ { 3 } = 0.880 \\ 902 & 10132 & 25.3 & 16 & \text { Y/ } X _ { 1 } , X _ { 2 } , X _ { 3 } = 0.884 \\ 986 & 11145 & 30.4 & 17 & \\ 909 & 9775 & 32.7 & 18 & \\ 945 & 9549 & 35.0 & 19 & \\ 866 & 10077 & 33.8 & 20 & \\ 1178 & 11550 & 29.4 & 21 & \\ 1230 & 10600 & 37.1 & 22 & \\ 1207 & 11280 & 42.9 & 23 & \\ 968 & 12100 & 32.2 & 24 & \\ 1118 & 12420 & 30.5 & 25 & \end{array}$

• A) \(\hat { Y } = 57.8 + 0.036 X _ { 1 } + 28.1 X _ { 3 }\)
• B) \(\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }\)
• C) \(\hat { Y } = 201.7 + 0.40 X _ { 1 } + 22.3 X _ { 3 }\)
• D) \(\hat { Y } = 308.6 + 29.9 X _ { 3 }\)

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Definitions:

Visual Field

The full extent of the area visible in the peripheral view when the eye is fixed on a central spot.

Blobs

Regions in the visual cortex that are sensitive to color, playing a role in the perception of color in visual stimuli.

Visual Cortex

The region of the brain that processes visual information, located in the occipital lobe.

Color Perception

The process by which the brain interprets wavelengths of light as different colors, relying on the interactions of photoreceptor cells in the eyes.