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 7.56SE
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 7.56SE
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 7.56SE
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
Basic Practice of Statistics (Instructor's)
- ons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 workarrow_forward2. The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car's age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Po + B₁Age + ε. A portion of the regression results is shown in the accompanying table. Standard Coefficients Intercept 21187.94 Error 733.42 t Stat p-value 28.89 1.56E-16 Age -1208.25 128.95 -9.37 2.41E-08 a. What is the estimate for B₁? Interpret this value. b. What is the sample regression equation? C. Predict the selling price of a 5-year-old sedan.arrow_forwardian income of $50,000. erty rate of 13. Using data from 50 workers, a researcher estimates Wage = Bo+B,Education + B₂Experience + B3Age+e, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. ni ogolloo bash 1 Standard Coefficients error t stat p-value Intercept 7.87 4.09 1.93 0.0603 Education 1.44 0.34 4.24 0.0001 Experience 0.45 0.14 3.16 0.0028 Age -0.01 0.08 -0.14 0.8920 a. Interpret the estimated coefficients for Education and Experience. b. Predict the hourly wage rate for a 30-year-old worker with four years of higher education and three years of experience.arrow_forward
- 1. If a firm spends more on advertising, is it likely to increase sales? Data on annual sales (in $100,000s) and advertising expenditures (in $10,000s) were collected for 20 firms in order to estimate the model Sales = Po + B₁Advertising + ε. A portion of the regression results is shown in the accompanying table. Intercept Advertising Standard Coefficients Error t Stat p-value -7.42 1.46 -5.09 7.66E-05 0.42 0.05 8.70 7.26E-08 a. Interpret the estimated slope coefficient. b. What is the sample regression equation? C. Predict the sales for a firm that spends $500,000 annually on advertising.arrow_forwardCan you help me solve problem 38 with steps im stuck.arrow_forwardHow do the samples hold up to the efficiency test? What percentages of the samples pass or fail the test? What would be the likelihood of having the following specific number of efficiency test failures in the next 300 processors tested? 1 failures, 5 failures, 10 failures and 20 failures.arrow_forward
- The battery temperatures are a major concern for us. Can you analyze and describe the sample data? What are the average and median temperatures? How much variability is there in the temperatures? Is there anything that stands out? Our engineers’ assumption is that the temperature data is normally distributed. If that is the case, what would be the likelihood that the Safety Zone temperature will exceed 5.15 degrees? What is the probability that the Safety Zone temperature will be less than 4.65 degrees? What is the actual percentage of samples that exceed 5.25 degrees or are less than 4.75 degrees? Is the manufacturing process producing units with stable Safety Zone temperatures? Can you check if there are any apparent changes in the temperature pattern? Are there any outliers? A closer look at the Z-scores should help you in this regard.arrow_forwardNeed help pleasearrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 4. One-Way ANOVA: Analyze the customer satisfaction scores across four different product categories to determine if there is a significant difference in means. (Hints: The null can be about maintaining status-quo or no difference among groups) H0 = H1=arrow_forward
- Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 2. Two-Sample T-Test: Compare the average sales revenue of two different regions to determine if there is a significant difference. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null) H0 = H1=arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 3. Paired T-Test: A company implemented a training program to improve employee performance. To evaluate the effectiveness of the program, the company recorded the test scores of 25 employees before and after the training. Determine if the training program is effective in terms of scores of participants before and after the training. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional, use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting the null) H0 = H1= Conclusion:arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. The data for the following questions is provided in Microsoft Excel file on 4 separate sheets. Please conduct these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to…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