Question ONE: Nine steel specimens were submerged in seawater at various temperatures, andthe corrosion rates were measured. The observed corrosion rates (y: dependent variable), inmm/year, and temperatures (x: independent variable), in ºC, for the nine steel specimens areshown in the following table. The sample average of x, the sample average of y, the three typesof sums of squares, and the sum of squared errors (SSE) based on the least-squares linear modelare also provided as below.SteelX:Y:The following summary statistics" werespecimen ID Temperatures Corrosion("C)calculated from the data with n = 9:rate(mm/year)SsΣ. (x-3485.502127.41.58SSyy = E – )² = 0.883%3D226.61.45326.01.13SS.y = E(x, – 7)V. - 7)= 19.249421.71.05515.00.99I = 17.756 °C6.14.90.96y = 1.024 mm/year11.30.828.70.68Based on the least-squares linear model, the sum898.20.56of the squares of errors (SSE) was computed as:n-9SSE = 0 - 9)² = 0.120-1(1) Compute the sample coefficient of correlation between corrosion rate (v) and temperature(x). What does the value of the correlation coefficient tell about the relationship betweencorrosion rate (v) and temperature (x)? Explain why.(2) Let ŷ = Bo + B, x be the least-squares linear regression model for predicting corrosionrate (y) from temperature (x). Compute the least-squares estimates ß, and ß,.(3) Compute the coefficient of the determination for the least-squares linear model youestimated. What does the value of the coefficient of the determination tell about thegoodness-of-fit of your model? Explain why.(4) Compute sp,, an estimate of the standard deviation of ßg.(5) Compute the 90% confidence interval for the true parameter B, based on the estimated Bg.(6) Can you state, at a significance level of 5%, that B, # 0 (i.e. Test Ho: B, = 0 vs. H:Bo # 0)? Report the P -value of this hypothesis test.

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Description: Question ONE: Nine steel specimens were submerged in seawater at various temperatures, andthe corrosion rates were measured. The observed corrosion rates (y: dependent variable), inmm/year, and temperatures (x: independent variable), in ºC, for the

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tes were measured. The observed corrosion rates (y: dependent mperatures (x: independent variable), in ºC, for the nine steel sp lowing table. The sample average of x, the sample average of y res, and the sum of squared errors (SSE) based on the least-squa d as below. Y: The following summary : calculated from the data w X: Temperatures Corrosion ('C) rate (ттуear) 1.58 27.4 26.6 1.45 26.0 1.13 SS,y = E-,(x, – 3)V 21.7 1.05 15.0 ī = 17.756 °C 0.99 14.9 0.96 y = 1.024 mm/year 11.3 0.82

tes were measured. The observed corrosion rates (y: dependent mperatures (x: independent variable), in ºC, for the nine steel sp lowing table. The sample average of x, the sample average of y res, and the sum of squared errors (SSE) based on the least-squa d as below. Y: The following summary : calculated from the data w X: Temperatures Corrosion ('C) rate (ттуear) 1.58 27.4 26.6 1.45 26.0 1.13 SS,y = E-,(x, – 3)V 21.7 1.05 15.0 ī = 17.756 °C 0.99 14.9 0.96 y = 1.024 mm/year 11.3 0.82

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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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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