The following estimated regression equation based on 10 observations was presented.ŷ = 29.1270 + 0.7906x1 + 0.3980x2(a)Develop a point estimate of the mean value of y when x1 = 190 and x2 = 350. (b)Develop a point estimate for an individual value of y when x1 = 190 and x2 = 350. (2) The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA.ŷ = −1.38 + 0.0234x1 + 0.00482x2wherex1 = high-school grade point averagex2 = SAT mathematics scorey = final college grade point average.(a)Interpret the coefficients in this estimated regression equation.(b)Predict the final college GPA for a student who has a high-school average of 83 and a score of 530 on the SAT mathematics test. A statistical program is recommended.Data contained in the DATAfile named PGADriving Dist was used to develop an estimated regression equation to predict the average number of yards per drive given the ball speed and the launchangle.t(a) Does the estimated regression equation provide a good fit to the data? Explain. (Round your answers to four decimal places.)Since R²are ---Select---the estimated regression equation |---Select---=2and Ra=a good fit.(b) An estimated regression equation was developed using only ball speed to predict the average number of yards per drive. Compare the fit obtained using just ball speed to the fit obtained usingball speed and the launch angle. (Round your answers to two decimal places.)The value of R² indicates that using just ball speed can account for% of the variability in total distance. The addition of launch angle ---Select--- the percentage toTherefore, the estimated regression equation using both ball speed and launch angle |---Select--- provide better predictions.%

Note:The problem has multiple questions As per the guidelines of the Q&A only the first question…

Answered: The following estimated regression…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The following estimated regression equation based on 10 observations was presented.

ŷ = 29.1270 + 0.7906x₁ + 0.3980x₂

(a)

Develop a point estimate of the mean value of y when

x₁ = 190 and x₂ = 350.

(b)

Develop a point estimate for an individual value of y when

x₁ = 190 and x₂ = 350.

(2)

The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA.

ŷ = −1.38 + 0.0234x₁ + 0.00482x₂

where

x₁	=	high-school grade point average
x₂	=	SAT mathematics score
y	=	final college grade point average.

(a)

Interpret the coefficients in this estimated regression equation.

(b)

Predict the final college GPA for a student who has a high-school average of 83 and a score of 530 on the SAT mathematics test.

A statistical program is recommended.
Data contained in the DATAfile named PGADriving Dist was used to develop an estimated regression equation to predict the average number of yards per drive given the ball speed and the launch
angle.t
(a) Does the estimated regression equation provide a good fit to the data? Explain. (Round your answers to four decimal places.)
Since R²
are ---Select---
the estimated regression equation |---Select---
=
2
and Ra
=
a good fit.
(b) An estimated regression equation was developed using only ball speed to predict the average number of yards per drive. Compare the fit obtained using just ball speed to the fit obtained using
ball speed and the launch angle. (Round your answers to two decimal places.)
The value of R² indicates that using just ball speed can account for
% of the variability in total distance. The addition of launch angle ---Select--- the percentage to
Therefore, the estimated regression equation using both ball speed and launch angle |---Select--- provide better predictions.
%

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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