Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 13.3, Problem 32E
a.
To determine
Construct a standardized residual plot.
Check whether the plot exhibit any unusual features.
b.
To determine
Check and explain whether it is reasonable to assume that the error distribution is approximately normal.
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Suppose that a sample of n = 12 pairs of X and Y scores has SSY = 90 and a Pearson correlation of r = +0.40. Does the regression equation predict a significant portion of the variance? Test with α = .05.(hint: SStotal = SSY; r2 = SSregression/SSTotal)
A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that
b1=1.4379 and Sb1=0.1397.
a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?
b. Construct a 95% confidence interval estimate of the population slope,
β1.
a. Determine the hypotheses for the test. Choose the correct answer below.
A.
H0:
β1=0
H1:
β1≠0
B.
H0:
β0≤0
H1:
β0>0
C.
H0:
β1≤0
H1:
β1>0
D.
H0:
β0≥0
H1:
β0<0
E.
H0:
β1≥0
H1:
β1<0
F.
H0:
β0=0
H1:
β0≠0
Compute the test statistic.
The test statistic is ?
(Round to two decimal places as needed.)
Determine the critical value(s).
The critical value(s) is(are) ?
(Use a comma to separate answers as needed.…
In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4.Click on the datafile logo to reference the data. Use Table 1 of Appendix B.
a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $
c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
Chapter 13 Solutions
Introduction To Statistics And Data Analysis
Ch. 13.1 - Let x be the size of a house (in square feet) and...Ch. 13.1 - Consider the variables and population regression...Ch. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - A sample of small cars was selected, and the...Ch. 13.1 - Prob. 6ECh. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 9ECh. 13.1 - Hormone replacement therapy (HRT) is thought to...
Ch. 13.1 - Consider the data and estimated regression line...Ch. 13.1 - A simple linear regression model was used to...Ch. 13.1 - Consider the accompanying data on x = Advertising...Ch. 13.2 - What is the difference between and b? What is the...Ch. 13.2 - The largest commercial fishing enterprise in the...Ch. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - An experiment to study the relationship between x...Ch. 13.2 - The paper The Effects of Split Keyboard Geometry...Ch. 13.2 - The authors of the paper Decreased Brain Volume in...Ch. 13.2 - Do taller adults make more money? The authors of...Ch. 13.2 - Researchers studying pleasant touch sensations...Ch. 13.2 - Prob. 24ECh. 13.2 - Acrylamide is a chemical that is sometimes found...Ch. 13.2 - Prob. 26ECh. 13.2 - Exercise 13.18 described a regression analysis...Ch. 13.2 - Consider the accompanying data on x = Research and...Ch. 13.2 - Prob. 29ECh. 13.2 - In anthropological studies, an important...Ch. 13.3 - The graphs accompanying this exercise are based on...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The article Vital Dimensions in Volume Perception:...Ch. 13.3 - Prob. 35ECh. 13.3 - An investigation of the relationship between x =...Ch. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - In Exercise 13.19, we considered a regression of y...Ch. 13.4 - Prob. 40ECh. 13.4 - A subset of data read from a graph that appeared...Ch. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.4 - The article first introduced in Exercise 13.34 of...Ch. 13.4 - The shelf life of packaged food depends on many...Ch. 13.4 - For the cereal data of the previous exercise, the...Ch. 13.4 - The article Performance Test Conducted for a Gas...Ch. 13.5 - Prob. 48ECh. 13.5 - Prob. 49ECh. 13.5 - A sample of n = 353 college faculty members was...Ch. 13.5 - Prob. 51ECh. 13.5 - Prob. 52ECh. 13.5 - The accompanying summary quantities for x =...Ch. 13.5 - Prob. 54ECh. 13.5 - Prob. 55ECh. 13.6 - Prob. 56ECh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - Prob. 3CRECh. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - The accompanying graphical display is similar to...Ch. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Consider the following data on y = Number of songs...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - Prob. 11CRECh. 13 - Prob. 12CRECh. 13 - Prob. 13CRECh. 13 - Prob. 14CRECh. 13 - The discharge of industrial wastewater into rivers...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - It is hypothesized that when homing pigeons are...Ch. 13 - Prob. 18CRECh. 13 - Prob. 57CRCh. 13 - Prob. 58CRCh. 13 - Prob. 59CRCh. 13 - The article Photocharge Effects in Dye Sensitized...Ch. 13 - Prob. 61CRCh. 13 - Prob. 62CRCh. 13 - Prob. 63CRCh. 13 - Prob. 64CRCh. 13 - Prob. 65CRCh. 13 - The article Improving Fermentation Productivity...Ch. 13 - Prob. 67CRCh. 13 - Prob. 68CRCh. 13 - Prob. 69CR
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- A sample of n = 120 scores were presented using the Tenacity (authority) scores to the following predictors: age gender, SES, tone of voice, and clothing. Using a two-tailed test at the 0.05 level of significance, a multiple regression analysis was computed: 1. tenacity and age (pvalue = 0.043); 2. tenacity and gender (pvalue = 0.102); 3. tenacity and SES (pvalue = 0.40); 4. tenacity and voice (pvalue = 0.001); 5. tenacity and clothing (value = 0.017); SOrs Using the pvalue, provide your DECISION, whether:Accept Ho or Reject Ho, Accept Haarrow_forwardIn exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B.Click on the datafile logo to reference the data. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$ b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $ c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).$ to $arrow_forwardWhich of the following scatterplots provides evidence that the condition of equal variance for inference for the slope of a regression line has not been met?arrow_forward
- A sample of n = 120 scores were presented using the Tenacity (authority) scores to the following predictors: age gender, SES, tone of voice, and clothing. Using a two-tailed test at the 0.05 level of significance, a multiple regression analysis was computed: 1. tenacity and voice (pvalue = 0.001); 2. tenacity and clothing (pvalue = 0.017); Using the pvalue, provide your DECISION, whether: Accept Ho or Reject Ho, Accept Haarrow_forwardA sample of n = 120 scores were presented using the Tenacity (authority) scores to the following predictors: age gender, SES, tone of voice, and clothing. Using a two-tailed test at the 0.05 level of significance, a multiple regression analysis was computed: 2. tenacity and gender (pvalue = 0.102); Using the pvalue, provide your DECISION, whether: Accept Ho or Reject Ho, Accept Haarrow_forwardA sample of n = 120 scores were presented using the Tenacity (authority) scores to the following predictors: age gender, SES, tone of voice, and clothing. Using a two-tailed test at the 0.05 level of significance, a multiple regression analysis was computed: 5. tenacity and clothing (value = 0.017); SOrs Using the pvalue, provide your DECISION, whether: Accept Ho or Reject Ho, Accept Haarrow_forward
- Listed below are paired data consisting of waist size in centimeters and Body Mass Index BMI from a random sample of 20 adult men selected from the population. At the a = 0.05 significance level, test the claim that there is positive linear correlation between waist size and Body Mass Indices in adult men, by answering questions a. thru e. below. That is, test the claim: ρ>0 This uses a Null Hypothesis of ρ =0 and an Alternative Hypothesis of ρ>0 WAIST BMI 120.4 33.3 107.8 28.0 120.3 45.4 97.2 28.4 95.1 25.9 112.0 31.1 78.0 20.1 103.5 32.7 89.7 25.8 112.0 36.5 95.0 25.8 115.3 34.5 118.8 37.4 92.6 26.1 75.5 19.3 101.8 29.9 92.5 27.4 100.8 31.4 82.8 21.0 92.9 28.5 a. What is the linear correlation coefficient r = ___________________________ b. What is the P-Value…arrow_forwardUse the following information from a multiple regression analysis. n=15 b1=2 b2=6 Sb1=1.4 Sb2=0.5 a. Which variable has the largest slope, in units of a t statistic? b. Construct a 90% confidence interval estimate of the population slope, β1. c. At the 0.10 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.arrow_forward
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