Concept explainers
Videos
a.
To find: The equation of the least-squares line for predicting a neuron's call response from its pure tone response.
To construct: The
To construct: The scatter plot with the point A which is the largest residual (either positive or negative) and also the point B that is an outlier in the x direction.
a.
Answer to Problem 7.54SE
The equation of the least-squares line for predicting a neuron's call response from its pure tone response is
Output using the MINITAB software is given below:
Output with marked point A and B using the MINITAB software is given below:
Explanation of Solution
The given data shows the pure-tone response and monkey call response values.
Calculation:
Software procedure:
Step by step procedure to find the equation of the least-squares line by using the MINITAB software:
- Choose Stat > Regression > Regression.
- In Responses, enter the column of Call.
- In Predictors, enter the column of Tone.
- Click OK.
Output using the MINITAB software is given below:
From the MINITAB output, it is clear that the regression equation is
Scatterplot:
Software procedure:
Step by step procedure to construct the scatter plots using the MINITAB software:
- Choose Graph > Scatter plot.
- Choose with regression and groups, and then click OK.
- Under Y variables, enter a column of Call.
- Under X variables, enter a column of Tone.
- Click OK.
From the scatterplot, it is observed that the plot shows no distinct pattern. Also, the x (pure-tone response) values increase then the corresponding y (monkey call response) values increase. Also, the points are moderately scattered. Thus, there is moderately
Also, from the scatterplot, it is observed that the largest residual is marked as point A(241,485) and also the outlier in the x direction point is marked as B(474,500).
b.
To explain: The influences of the points A and B for the
b.
Answer to Problem 7.54SE
The outlier and residual is removed then the correlation decreases.
Explanation of Solution
Calculation:
Correlation: With points A and B
Step by step procedure to obtain the correlation using the MINITAB software:
- Select Stat > Basic Statistics > Correlation.
- In Variables, select X, and Y from the box on the left.
- Click OK.
Output using the MINITAB software is given below:
From the output, the correlation with points A and B is 0.639.
Correlation: Without points A and B.
Step by step procedure to obtain the correlation using the MINITAB software:
- Select Stat > Basic Statistics > Correlation.
- In Variables, select X, and Y from the box on the left.
- Click OK.
Output using the MINITAB software is given below:
From the output, the correlation without points A and B is 0.359.
The correlation with points A and B is 0.639 and the correlation without points A and B is 0.359. Also, from the scatterplot in part (a), it is observed that the outlier and residual deviate from linear pattern of the other points.
Thus, it can be concluded that if the outlier and residual are removed then the correlation decreases. Thus, the outlier and residual influence the correlation.
c.
To explain: The influences of the points A and B for the least-squares line.
c.
Answer to Problem 7.54SE
The effect of the outlier and residual influences on the line is small.
Explanation of Solution
Calculation:
Regression: With Fidelity Gold Fund.
Step by step procedure to obtain the regression using the MINITAB software:
- Choose Stat > Regression > Regression.
- In Responses, enter the column of y.
- In Predictors, enter the column of x.
- Click OK.
Output using the MINITAB software is given below:
From the output, the least-squares line for predicting y from x with points A and B is
Regression: Without points A and B.
Step by step procedure to obtain the regression using the MINITAB software:
- Choose Stat > Regression > Regression.
- In Responses, enter the column of y.
- In Predictors, enter the column of x.
- Click OK.
Output using the MINITAB software is given below:
From the output, the least-squares line for predicting y from x without points A and B is
Scatter plot:
Step by step procedure to construct the scatter plots with two regression line using the MINITAB software:
- Choose Graph > Scatter plot.
- Choose with regression and groups, and then click OK.
- Under Y variables, enter a column of Y.
- Under X variables, enter a column of X.
- Click OK.
Output using the MINITAB software is given below:
Observation:
From the scatterplot with two regression lines, it is observed that the horizontal axis represents the pure-tone response values and vertical axis represents the monkey call response values. Also, the regression line with all points is marked with solid line and the regression line without points A and B is marked with dashed line.
Also, it is observed that the effect of the points A and B on the line is small. Hence, the residual and outlier was not particularly extreme in the pure-tone response.
Thus, it can be concluded that the outlier and residual do not influence the least-square regression line.
Want to see more full solutions like this?
Chapter 7 Solutions
Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access)
- SCIE 211 Lab 3: Graphing and DataWorksheetPre-lab Questions:1. When should you use each of the following types of graphs? Fill answers in the table below.Type of Graph Used to showLine graphScatter plotBar graphHistogramPie Chart2. Several ways in which we can be fooled or misled by a graph were identified in the Lab 3Introduction. Find two examples of misleading graphs on the Internet and paste them below. Besure to identify why each graph is misleading. Data Charts:Circumference vs. Diameter for circular objectsDiameter Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanCircumference Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanScatter Plot Graph – Circumference Vs. DiameterIdentify 2 points of the Trendline.Y1 = ________ Y2 = _________X1 = ________ X2 = _________Calculate the Slope of the Trendline = Post-lab Questions:1. Answer the questions below. You will need to use the following equation to answer…arrow_forwardThe U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2014.H 0: p H a: p b. If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test (to 4 decimals)?arrow_forwardA company manages an electronic equipment store and has ordered 200200 LCD TVs for a special sale. The list price for each TV is $200200 with a trade discount series of 6 divided by 10 divided by 2.6/10/2. Find the net price of the order by using the net decimal equivalent.arrow_forward
- According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 10 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 6 flights are on time. (d) Find and interpret the probability that fewer than 6 flights are on time. (e) Find and interpret the probability that at least 6 flights are on time. (f) Find and interpret the probability that between 4 and 6 flights, inclusive, are on time.arrow_forwardShow how you get critical values of 1.65, -1.65, and $1.96 for a right-tailed, left- tailed, and two-tailed hypothesis test (use a = 0.05 and assume a large sample size).arrow_forwardSuppose that a sports reporter claims the average football game lasts 3 hours, and you believe it's more than that. Your random sample of 35 games has an average time of 3.25 hours. Assume that the population standard deviation is 1 hour. Use a = 0.05. What do you conclude?arrow_forward
- Suppose that a pizza place claims its average pizza delivery time is 30 minutes, but you believe it takes longer than that. Your sample of 10 pizzas has an average delivery time of 40 minutes. Assume that the population standard deviation is 15 minutes and the times have a normal distribution. Use a = 0.05. a. What are your null and alternative hypotheses? b. What is the critical value? c. What is the test statistic? d. What is the conclusion?arrow_forwardTable 5: Measurement Data for Question 9 Part Number Op-1, M-1 Op-1, M-2 | Op-2, M-1 Op-2, M-2 | Op-3, M-1 Op-3, M-2 1 21 20 20 20 19 21 2 24 23 24 24 23 24 3 4 5 6 7 8 9 10 11 21 12 8222332 201 21 20 22 20 22 27 27 28 26 27 28 19 18 19 21 24 21 22 19 17 18 24 23 25 25 23 26 20 20 18 19 17 13 23 25 25 2 3 3 3 3 2 3 18 18 21 21 23 22 24 22 20 19 23 24 25 24 20 21 19 18 25 25 14 24 24 23 25 24 15 29 30 30 28 31 16 26 26 25 26 25 17 20 20 19 20 20 843882388 20 18 25 20 19 25 25 30 27 20 18 19 21 19 19 21 23 19 25 26 25 24 25 25 20 19 19 18 17 19 17 Question 9 A measurement systems experiment involving 20 parts, three operators (Op-1, Op-2, Op-3), and two measure- ments (M-1, M-2) per part is shown in Table 5. (a) Estimate the repeatability and reproducibility of the gauge. (b) What is the estimate of total gauge variability?" (c) If the product specifications are at LSL = 6 and USL 60, what can you say about gauge capability?arrow_forwardQuestion 5 A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a process. (a) If three-sigma limits are used, find the sample size for the control charte 2 (b) Use the Poisson approximation to the binomial to find the probability of type I error. (c) Use the Poisson approximation to the binomial to find the probability of type II error if the process fraction defective is actually p = 0.20.arrow_forward
- Question 8 Ten parts are measured three times by the same operator in a gauge capability study. The data are shown in Table 4. (a) Describe the measurement error that results from the use of this gauge. I (b) Estimate total variability and product variability. (c) What percentage of total variability is due to the gauge? (d) If specifications on the part are at 100±15, find the P/T ratio for this gauge. Comment on the adequacy of the gauge. 3 Table 4: Measurement Data for Question 8 Part Number Measurement 1 Measurement 2 Measurement 3 1 2 100 95 101 100 93 97 3 101 103 100 4 96 95 97 5 98 98 96 6 99 98 98 7889 95 97 98 100 99 98 100 100 97 10 100 98 98 99arrow_forwardQuestion 6 The data shown in Table 3 are and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). Perform a process capability analysis using and R charts for the data from Table 3. Table 3: Data for Question 6 Sample Number R | Sample Number I Ꭱ 1 34.5 3 13 35.4 8 2 34.2 4 14 34.0 6 ∞∞ 31.6 15 37.1 5 4 31.5 4 16 34.9 7 56789 35.0 5 17 33.5 4 34.1 6 18 31.7 3 32.6 4 19 34.0 8 33.8 3 20 35.1 4 34.8 7 10 33.6 8 11 31.9 3 12 38.6 9 2232 21 33.7 2 32.8 1 33.5 24 34.2 2 32 3arrow_forwardQuestion 1 The commercial loan operation of a financial institution has a standard for processing new loan applications in 24 hours. Table 1 shows the number of applications processed each day for the last 20 days and the number of applications that required more than 24 hours to complete. Table 1: Loan Application Data for Question 1 Day Applications Late Day Applications Late 1 200 3 11 219 0 2 250 4 12 238 10 3 240 2 13 250 4 4 300 5 14 302 6 5 200 2 15 219 20 6 250 4 16 246 3 7 246 3 17 251 6 8 258 5 18 273 7 9 275 2 19 245 3 10 274 1 20 260 (a) Set up the fraction nonconforming control chart for this process. Use the variable-width control limit approach. Plot the preliminary data in Table 1 on the chart. Is the process in statistical control? (b) Assume that assignable causes can be found for any out-of-control points on this chart. What center line should be used for process monitoring in the next period, and how should the control limits be calculated?arrow_forward
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman