Business Statistics: A First Course (8th Edition)
8th Edition
ISBN: 9780135177785
Author: David M. Levine, Kathryn A. Szabat, David F. Stephan
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
error_outline
This textbook solution is under construction.
Students have asked these similar questions
Interest rates for home mortgages have, in general, declined during recent months. With the apparent favorable influence for
new-home building, there seems to be a clear relationship between x = the prevailing mortgage interest rate and y = the number
of new houses being built per month in a Midwestern city over a period of 18 months. A scatterplot of the data collected shows
that the linear model is appropriate. The equation of the least-squares regression line is Number of new houses = 672.89-
30.65 x Interest rate and ² = 0.49.
What is the correlation coefficient between Interest rate and Number of new houses being built? (Give your answer to one
decimal place.)
Please help with unanswered questions. Thank you!
We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation
information at the firm-level. We are interested in predicting a company's sales based on the CEO's
salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable
salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to
estimate the linear regression
sales; = a + ßsalary; + ei
and get the following regression results:
regress sales salary
.
Source
Model
Residual
Total
sales
salary
_cons
SS
337920405
2.3180e+10
2.3518e+10
df
1
207
208
Coef. Std. Err.
.9287785 .5346574
5733.917 1002.477
MS
337920405
111980203
113066454
t
Number of obs
F(1, 207)
Prob> F
R-squared
Adj R-squared
Root MSE
P>|t|
1.74 0.084
5.72 0.000
209
3.02
-.1252934
3757.543
0.0838
0.0144
0.0096
10582
[95% Conf. Interval]
1.98285
7710.291
This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary.
Suppose a CEO of a company…
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 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_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardWe have data from 209 publicly traded companies (circa 2010) indicating sales and compensation information at the firm-level. We are interested in predicting a company's sales based on the CEO's salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to estimate the linear regression sales; = a + ßsalary; + ei and get the following regression results: . regress sales salary Source Model Residual Total sales salary cons SS 337920405 2.3180e+10 2.3518e+10 df 1 207 208 Coef. Std. Err. .9287785 .5346574 5733.917 1002.477 MS 337920405 111980203 113066454 Number of obs F (1, 207) Prob > F R-squared t P>|t| = Adj R-squared = Root MSE 1.74 0.084 5.72 0.000 = = -.1252934 3757.543 = 209 3.02 0.0838 0.0144 0.0096 10582 [95% Conf. Interval] 1.98285 7710.291 This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary. Interpret the…arrow_forward
- The manager of the Ramona Inn Hotel near Cloverleaf Stadium believes that how well the local Blue Sox professional baseball team is playing has an impact on the occupancy rate at the hotel during the summer months. Following are the number of victories for the Blue Sox (in a 162-game schedule) for the past 8 years and the hotel occupancy rates: Develop a linear regression model for these data and forecast the occupancy rate for next year if the Blue Sox win 88 gamesarrow_forwardWe have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.arrow_forwardA researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix. 1) a) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Explain your decision by providing its statistical basis.arrow_forward
- A researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix.1) b) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Establish the simple linear regression model using the argument of your choice and write the equation for the model. Interpret b0 and b1.1) c) Test whether there is a statistically significant and linear relationship between the independent variable and the dependent variable by establishing the relevant…arrow_forwardA major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. Data were collected that show the number of new customers added during each quarter between 2015 and 2018. A multiple regression model was developed with the number of new customers as the dependent and the following four independent variables: Period (1, …, 16): A variable that measures the trend; Q1 = 1 for first quarter, Q1 = 0 otherwise; Q2 = 1 for second quarter, Q2 = 0 otherwise; Q3 = 1 for third quarter, Q3 = 0 otherwise. Questions: 1. Explain each of the four slopes (Period, Q1, Q2, Q3). 2. How many new customers would you expect in the second quarter of the following year (2019)?arrow_forwardArmer Company is accumulating data to use in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested the use of linear regression to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis follow: Month Maintenance Cost Machine Hours Jan. $ 4,200 480 Feb. 3,000 320 Mar. 3,600 400 Apr. 2,820 300 May 4,350 500 June 2,960 310 July 3,030 320 Aug. 4,470 520 Sept. 4,260 490 Oct. 4,050 470 Nov. 3,300 350 Dec. 3,160 340 Sum $ 43,200 4,800 Average $ 3,600 $ 400 Average cost per hour $ 9.00 a (intercept) $ 684.65 b (coefficient) 7.2884 Standard error of the estimate 34.469 R-squared 0.99724 t-value for b 60.105…arrow_forward
- Suppose a new point was added to your data: a wine that is 20% alcohol that contains 0calories. How will that affect the value of r and the slope of the regression line? (Nocalculation needed)arrow_forwardA county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y = b₁x + bowhere y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the following results were obtained: y = 74.80 + 17.80x Give a practical interpretation of the estimate of the slope of the least squares line. For each additional room in the house, we estimate the appraised value to increase $74,800. For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 17.80 rooms. For a house with O rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the…arrow_forwardthe scatter plot displays the number of pretzels students could grab with their dominant hand and their handspan, measured in centimeters. the equation of the line y=-14.7+1.59x is called the least-squares regression line because itarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY