Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Textbook Question
Chapter A.3, Problem 61E
Answer true or false to the following statements and explain your answers.
- a. If the F-test for the utility of a multiple linear regression rejects the null hypothesis, then all the population regression coefficients are different from 0.
- b. If the F-test for the utility of a multiple linear regression does not reject the null hypothesis, we can conclude that there is no relationship whatsoever between the response variable and the predictor variables.
- c. If the value of the F-statistic for testing the utility of the multiple linear regression is close to 0, the value of the coefficient of multiple determination will be close to 0.
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Answer true or false to the following statements and explain your answers.
a. If the F-test for the utility of a multiple linear regression rejects the null hypothesis, then all the population regression coefficients are different from 0.
b. If the F-test for the utility of a multiple linear regression does not reject the null hypothesis, we can conclude that there is no relationship whatsoever between the response variable and the predictor variables.
c. If the value of the F-statistic for testing the utility of the multiple linear regression is close to 0, the value of the coefficient of multiple determination will be close to 0.
Answer true or false to each of the following statements and explain your answers.a. Correlations among values of the response variable have no effect whatsoever on statistical inferences based upon the t-statistics and F-statistic used in multiple linear regression.b. When there are errors in the measurements of the predictor variables, statistical inferences in regression analysis become less reliable.c. A nonrepresentative sample of the population of interest will have no effect on the regression model that is obtained.
We are interested in the relationship between mid-term exam scores and final exam scores. The Final Exam score is the dependent variable and Midterm score is the independent variable. Use the simple
regression output on below to answer the question below. Use a significance level of 0.05 for all hypothesis tests and intervals.
Adam Smith scored a 70 on his Midterm. Therefore, Adam should expect to score at least
and no more than
on the Final exam with a 95% confidence.
O Bivariate Fit of Final Exam By Midterm
100
90
80
70
60
50
55
60
65
70
75
100
80
Midterm
85
90
95
Parameter Estimates
Term
Estimate Std Error t Ratio Prob> |t| Lower 95% Upper 95%
Intercept 31.738559
Midterm
10.26099
3.09
0.0031*
<.0001*
11.166522
52.310596
0.61916 0.128514
4.82
0.3615044
0.8768157
Upper 95%
Indiv Final ...
Predicted
Lower 95%
Upper 95%
Lower 95%
Student Midterm Final Exam
Final Exam
Mean Final
Mean Final ... Indiv Final ...
...
70
75.07976245 71.391337991 78.768186908 53.411179985 96.748344914
O…
Chapter A Solutions
Introductory Statistics (10th Edition)
Ch. A.1 - A. 1 Regarding linear equations in two or more...Ch. A.1 - Fill in the blanks. a. The graph of a linear...Ch. A.1 - Consider a linear equation y = b0 + b1x1 + b2x2. ...Ch. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Banquet Room Rental. The banquet room at the...Ch. A.1 - Prob. 8ECh. A.1 - In each of Exercises A.9A.12, a. determine the...Ch. A.1 - In each of Exercises A.9A.12, a. determine the...
Ch. A.1 - In each of Exercises A.9A.12, a. determine the...Ch. A.1 - In each of Exercises A.9A.12, a. determine the...Ch. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - In each of Exercises A.13A.22, you are given the...Ch. A.1 - Prob. 17ECh. A.1 - Prob. 18ECh. A.1 - In each of Exercises A.13A.22, you are given the...Ch. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - In each of Exercises A.13A.22, you are given the...Ch. A.1 - In each of Exercises A.23A.30, we have identified...Ch. A.1 - Prob. 24ECh. A.1 - Prob. 25ECh. A.1 - Prob. 26ECh. A.1 - In each of Exercises A.23A.30, we have identified...Ch. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Prob. 30ECh. A.1 - Why is it often preferable to use more than one...Ch. A.1 - Grade Prediction. The Statistics Department at a...Ch. A.1 - Prob. 33ECh. A.1 - Blood Pressure Medication. A medical researcher...Ch. A.1 - Infant Mortality Rate. A social scientist wants to...Ch. A.2 - Regarding a scatterplot matrix: a. Identify two of...Ch. A.2 - Regarding the criterion used to decide tits a set...Ch. A.2 - Prob. 38ECh. A.2 - Regarding the variables in a multiple linear...Ch. A.2 - Answer true or false to the following statements...Ch. A.2 - In each of Exercises A.41 and A.42, a. construct...Ch. A.2 - In each of Exercises A.41 and A.42, a. construct...Ch. A.2 - Advertising and Sales. A household-appliance...Ch. A.2 - Corvette Prices. The data on age and price for 10...Ch. A.2 - Graduation Kales. Graduation rates and what...Ch. A.2 - Custom Home Resales. Hanna Properties specializes...Ch. A.2 - Advertising and Sales. Refer to Exercise A.43. Use...Ch. A.2 - Prob. 48ECh. A.2 - Graduation Rates. Refer to Exercise A.45. Use the...Ch. A.2 - Custom Home Resales. Refer to Exercise A.46. Use...Ch. A.3 - Fill in the blanks. a. A measure of total...Ch. A.3 - In this section we introduced a descriptive...Ch. A.3 - Suppose x1, x2, and x3 are predictor variables and...Ch. A.3 - State the four conditions required for making...Ch. A.3 - In each of Exercises A.55A.59, assume the...Ch. A.3 - In each of Exercises A.55A.59, assume the...Ch. A.3 - In each of Exercises A.55A.59, assume the...Ch. A.3 - Prob. 58ECh. A.3 - In each of Exercises A.55A.59, assume the...Ch. A.3 - Fill in the blanks. a. When a sum of squares is...Ch. A.3 - Answer true or false to the following statements...Ch. A.3 - For a particular multiple linear regression...Ch. A.3 - For a particular multiple linear regression...Ch. A.3 - Advertising and Sales. Refer to Exercise A.43 on...Ch. A.3 - Corvette Prices. Refer to Exercise A.44 on page...Ch. A.3 - Graduation Rates. Refer to Exercise A.45 on page...Ch. A.3 - Custom Home Resales. Refer to Exercise A.46 on...Ch. A.3 - Advertising and Sales. Refer to Exercise A.43 on...Ch. A.3 - Corvette Prices. Refer to Exercise A.44 on page...Ch. A.3 - Graduation Rates. Refer to Exercise A.45 on page...Ch. A.3 - Custom Home Resales. Refer to Exercise A.46 on...Ch. A.3 - Suppose that R2 = 1 for a data set. What can you...Ch. A.3 - Suppose that R2 = 0 for a data set. What can you...Ch. A.3 - Use the regression identity for multiple linear...Ch. A.4 - Explain why the predictor variables are useless as...Ch. A.4 - Prob. 76ECh. A.4 - What test statistic is used for a hypothesis test...Ch. A.4 - Answer line or false to the following statements...Ch. A.4 - Advertising and Sales. Refer to Exercise A.43 oil...Ch. A.4 - Prob. 80ECh. A.4 - Graduation Rates. Refer to Exercise A.45 on page...Ch. A.4 - Custom-Home Resales. Refer to Exercise A.46 on...Ch. A.4 - Advertising and Sales. Referring to Exercise A.79,...Ch. A.4 - Prob. 84ECh. A.4 - Graduation Rates. Referring to Exercise A.81, use...Ch. A.4 - Prob. 86ECh. A.5 - What two regression inferences did we discuss in...Ch. A.5 - Prob. 88ECh. A.5 - A sample multiple linear regression equation...Ch. A.5 - Answer true or false to the following statements...Ch. A.5 - Advertising and Sales. Refer to Exercise A.43 on...Ch. A.5 - Corvette Prices. Refer to Exercise A.44 on page...Ch. A.5 - Graduation Rates. Refer to Exercise A.45 on page...Ch. A.5 - Custom-Home Resales. Refer to Exercise A.46 on...Ch. A.5 - Advertising and Sales. Referring to Exercise A.91,...Ch. A.5 - Corvette Sales. Referring to Exercise A.92, use...Ch. A.5 - Graduation Rates. Referring to Exercise A.93, use...Ch. A.5 - Custom-Home Resales. Referring to Exercise A.94,...Ch. A.6 - Fill in the blanks. a. In multiple linear...Ch. A.6 - Describe the difference between a residual and a...Ch. A.6 - Fill in the blanks. a. In multiple linear...Ch. A.6 - Answer true or false to the following statements...Ch. A.6 - Prob. 103ECh. A.6 - Corvette Prices. Refer to Exercise A.44 on page...Ch. A.6 - Advertising and Sales. Refer to Exercise A.43 on...Ch. A.6 - Corvette Prices. Refer to Exercise A.44 on page...Ch. A.6 - Graduation Rates. Refer to Exercise A.45 on page...Ch. A.6 - Custom-Homes Resales. Refer to Exercise A.46 on...Ch. A - For a linear equation y = b0 + b1x1 + b2x2 + b3x3,...Ch. A - Consider the linear equation y = 5 + 4x1 3x2. a....Ch. A - Answer true or false to each of the following...Ch. A - What kind of plot is useful for deciding whether...Ch. A - Prob. 5RPCh. A - Prob. 6RPCh. A - Regarding multiple linear regression analysis: a....Ch. A - Prob. 8RPCh. A - For each of the following sums of squares in...Ch. A - Prob. 10RPCh. A - Prob. 11RPCh. A - Suppose x1 and x2 are predictor variables for a...Ch. A - Fill in the blanks. a. The F-statistic for a test...Ch. A - Answer true or false to each of the following...Ch. A - Which interval is wider: (a) the 95% confidence...Ch. A - What plots did we use in this module to decide...Ch. A - Regarding analysis of residuals, decide in each...Ch. A - Annual Income. The Census Bureau collects data on...Ch. A - Annual Income. Refer to Problem 18 and the...Ch. A - Annual Income. Refer to Problem 18, Outputs...Ch. A - Recall from Chapter 1 (page 34 of your text) that...Ch. A - At the beginning of this module on page A-0, we...
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardAnswer true or false to the following statements and explain your answers.a. The sample regression coefficients exactly equal the population regression coefficients.b. It is possible to determine all the features of high dimensional data by projecting the data to two-dimensional plots.c. The sample multiple linear regression equation cannot be used to predict the value of the response variable at values of the predictor variables for which we have no observations.arrow_forwardYou initially said that the most appropriate statistical analysis for the data is a one sample means t test. Would a one sample t test be more appropriate than a regression?arrow_forward
- . Researchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test? (A) The p-value of 0.04 indicates that 4% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass. (B) The p-value of 0.04 indicates that 16% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass. (C) The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that college athletes with higher lean body mass tend to have higher…arrow_forwardA researcher wants to predict the effect of the number of times a person eats every day and the number of times they exercise on BMI. What statistical test would work best? A. Pearson's R B. Spearman Rho C. Linear regression D. Multiple regressionarrow_forwardAnswer true or false to each of the following statements and explain your answers.a. Statistical methods designed for a particular set of assumptions may not perform well if the assumptions are violated.b. The presence of outliers in the values of the response variable can result in decreased values of the t-statistics for the utility of individual predictor variables.c. Generally, a regression model will predict as well or better for a new set of data than for the data from which it was developed.arrow_forward
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