For this problem, use the multiple regression equation below to complete parts (a) and(b). Yi=10+5X1i+3X2i a. Interpret the meaning of the slopes. A.IfX1increases one unit, Y increases 3 units. IfX2increases one unit, Y increases 5 units. B.IfX1increases one unit, Y increases 5 units. IfX2increases one unit, Y increases 3 units. C.IfX2is constant, whenX1increases one unit, Y increases 5 units. IfX1is constant, whenX2increases one unit, Y increases 3 units. D.IfX2is constant, whenX1increases one unit, Y increases 3 units. IfX1is constant, whenX2increases one unit, Y increases 5 units.b. Interpret the meaning of the Y-intercept. A.The Y-intercept 5 is the estimate of the mean value of Y ifX1andX2are both 0. B.The Y-intercept 5 is the estimate of the mean value of Y ifX1is 0. C.The Y-intercept 10 is the estimate of the mean value of Y ifX1andX2are both 0. D.The Y-intercept 10 is the estimate of the mean value of Y ifX1is 0.

Given data: The given multiple regression equation is : Yi=10+5X1i+3X2i To find: a.Interpret the…

Answered: For this problem, use the multiple…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 92E

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For this problem, use the multiple regression equation below to complete parts (a) and

(b).

Yi=10+5X1i+3X2i

a. Interpret the meaning of the slopes.

increases one unit, Y increases 3 units. If

increases one unit, Y increases 5 units.

increases one unit, Y increases 5 units. If

increases one unit, Y increases 3 units.

is constant, when

increases one unit, Y increases 5 units. If

is constant, when

increases one unit, Y increases 3 units.

is constant, when

increases one unit, Y increases 3 units. If

is constant, when

increases one unit, Y increases 5 units.

b. Interpret the meaning of the Y-intercept.

The Y-intercept 5 is the estimate of the mean value of Y if

and

are both 0.

The Y-intercept 5 is the estimate of the mean value of Y if

is 0.

The Y-intercept 10 is the estimate of the mean value of Y if

and

are both 0.

The Y-intercept 10 is the estimate of the mean value of Y if

is 0.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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