Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 7.2, Problem 13E
To determine
Find the equation of the least-squares line to predict firmness from pectin concentration.
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A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed.
Find the standard error of estimate for the regression equation.
How big would the standard error be if the sample size were n = 30.
In many fast food restaurants, there is a strong correlation between a menu item's fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menu items at a well-known fast food restaurant, the fat content and calorie content were measured. We decide to fit the least-squares regression line to the data, with fat content ( x) as the explanatory variable and calorie content ( y) as the response variable. A scatterplot of the data (with regression line included) and a summary of the data are provided. One of the menu items is a hamburger with 117 grams of fat and 1520 calories.
r = 0.979 (correlation between x and y)
= 40.35 grams (mean of the values of x)
= 662.88 calories (mean of the values of y)
= 27.99 grams (standard deviation of the values of x)
= 324.90 calories (standard deviation of the values of y)
Refer to the example data point (117 grams, 1520 calories). What is the residual corresponding to this…
Given are five observations for two variables, x and y.
xi
3
8
12
18
20
yi
54
57
50
24
11
-select your answer choices-
b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)
Chapter 7 Solutions
Statistics for Engineers and Scientists
Ch. 7.1 - Compute the correlation coefficient for the...Ch. 7.1 - For each of the following data sets, explain why...Ch. 7.1 - For each of the following scatterplots, state...Ch. 7.1 - True or false, and explain briefly: a. If the...Ch. 7.1 - In a study of ground motion caused by earthquakes,...Ch. 7.1 - A chemical engineer is studying the effect of...Ch. 7.1 - Another chemical engineer is studying the same...Ch. 7.1 - Tire pressure (in kPa) was measured for the right...Ch. 7.1 - Prob. 10ECh. 7.1 - The article Drift in Posturography Systems...
Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - A scatterplot contains four points: (2, 2), (1,...Ch. 7.2 - Each month for several months, the average...Ch. 7.2 - In a study of the relationship between the Brinell...Ch. 7.2 - A least-squares line is fit to a set of points. If...Ch. 7.2 - Prob. 4ECh. 7.2 - In Galtons height data (Figure 7.1, in Section...Ch. 7.2 - In a study relating the degree of warping, in mm....Ch. 7.2 - Moisture content in percent by volume (x) and...Ch. 7.2 - The following table presents shear strengths (in...Ch. 7.2 - Structural engineers use wireless sensor networks...Ch. 7.2 - The article Effect of Environmental Factors on...Ch. 7.2 - An agricultural scientist planted alfalfa on...Ch. 7.2 - Curing times in days (x) and compressive strengths...Ch. 7.2 - Prob. 13ECh. 7.2 - An engineer wants to predict the value for y when...Ch. 7.2 - A simple random sample of 100 men aged 2534...Ch. 7.2 - Prob. 16ECh. 7.3 - A chemical reaction is run 12 times, and the...Ch. 7.3 - Structural engineers use wireless sensor networks...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - The coefficient of absorption (COA) for a clay...Ch. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Three engineers are independently estimating the...Ch. 7.3 - In the skin permeability example (Example 7.17)...Ch. 7.3 - Prob. 12ECh. 7.3 - In a study of copper bars, the relationship...Ch. 7.3 - Prob. 14ECh. 7.3 - In the following MINITAB output, some of the...Ch. 7.3 - Prob. 16ECh. 7.3 - In order to increase the production of gas wells,...Ch. 7.4 - The following output (from MINITAB) is for the...Ch. 7.4 - The processing of raw coal involves washing, in...Ch. 7.4 - To determine the effect of temperature on the...Ch. 7.4 - The depth of wetting of a soil is the depth to...Ch. 7.4 - Good forecasting and control of preconstruction...Ch. 7.4 - The article Drift in Posturography Systems...Ch. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - A windmill is used to generate direct current....Ch. 7.4 - Two radon detectors were placed in different...Ch. 7.4 - Prob. 11ECh. 7.4 - The article The Selection of Yeast Strains for the...Ch. 7.4 - Prob. 13ECh. 7.4 - The article Characteristics and Trends of River...Ch. 7.4 - Prob. 15ECh. 7.4 - The article Mechanistic-Empirical Design of...Ch. 7.4 - An engineer wants to determine the spring constant...Ch. 7 - The BeerLambert law relates the absorbance A of a...Ch. 7 - Prob. 2SECh. 7 - Prob. 3SECh. 7 - Refer to Exercise 3. a. Plot the residuals versus...Ch. 7 - Prob. 5SECh. 7 - The article Experimental Measurement of Radiative...Ch. 7 - Prob. 7SECh. 7 - Prob. 8SECh. 7 - Prob. 9SECh. 7 - Prob. 10SECh. 7 - The article Estimating Population Abundance in...Ch. 7 - A materials scientist is experimenting with a new...Ch. 7 - Monitoring the yield of a particular chemical...Ch. 7 - Prob. 14SECh. 7 - Refer to Exercise 14. Someone wants to compute a...Ch. 7 - Prob. 16SECh. 7 - Prob. 17SECh. 7 - Prob. 18SECh. 7 - Prob. 19SECh. 7 - Use Equation (7.34) (page 545) to show that 1=1.Ch. 7 - Use Equation (7.35) (page 545) to show that 0=0.Ch. 7 - Prob. 22SECh. 7 - Use Equation (7.35) (page 545) to derive the...
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- A company trains its employees with instructional videos and claims that the amount of time, in hours, spent training is linearly related to an increase in productivity. The company selected a random sample of five employees to test its claim. The data were used to create the computer output for a least-squares linear regression, shown in the table. Variable DF Estimate SE Intercept 1 3.6 1.1489 Hours 1 0.8 0.3464 Which of the following is the correct test statistic and number of degrees of freedom? t=2.31 with 4 degrees of freedom A t=2.31 with 3 degrees of freedom B t=2.31 with 5 degrees of freedom C t=3.13 with 1 degree of freedom D t=3.13 with 3 degrees of freedom Earrow_forward(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?arrow_forwardIs CEO compensation related to a company's performance? To test whether CEO compensation and a company's stock performance are related, a financial analyst collected data on 12 randomly selected, publicly traded companies. For each company, the analyst looked at two variables: the percent change in stock price over the past five years (which she denoted x ) and the percent change in CEO compensation over the past five years (which she denoted y ). For these 12 companies, the least-squares regression equation relating the two variables was =y+−0.1650.046x , and the standard error of the slope of this least-squares regression line was approximately 0.028 . Using her information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope β1 . (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the…arrow_forward
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