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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

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Question

The following data has been collected on the relationship between concrete compressive
strength, Y (MPa), and initial water to cement ratio, X (by weight);
x 0.40 0.45 0.50 0.55 0.60 0.65
y 35.7 32.4 33.1 27.4 21.6 23.8
for which the following sums have been computed; X
xi = 3.15,
X
x2
i = 1.6975,
X
yi = 174,
X
y2
i = 5203.62,
X
xiyi = 88.91001
a) Find the straight line of best fit through the data.
b) Establish a 95% confidence interval on the true value of 0. Assume that the residuals
are normally distributed with constant mean zero and constant variance.
c) Is the linear relationship between Y and X significant? Test at a 95% confidence level.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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