EBK BUSINESS STATISTICS
7th Edition
ISBN: 8220102743984
Author: STEPHAN
Publisher: PEARSON
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45. Table 1.2 shows the mean annual compensation of construction
workers.
bab Abor Cesaione
TABLE 1.2 Construction Workers' Average
Annual Compensation
Annual Total Compensation
(dollars)
Year
1999
42,598
2000
44,764
2001
47,822
2002
48,966
Source: U.S. Bureau of the Census, Statistical Abstract of the United States,
2004-2005.
(a) Find the linear regression equation for the data.
(b) Find the slope of the regression line. What does the slope
represent?
(c) Superimpose the graph of the linear regression equation on a
scatter plot of the data.
(d) Use the regression equation to predict the construction workers'
average annual compensation in the year 2008.
Tabl
A researcher wants to investigate the influence of the average no. of nights spent per year by the tourists from Japan on the average amount spent by them. Table 3 shows the related data obtained from the Department of Statistics Malaysia website. Table 4 shows a portion of Microsoft Excel output for the regression analysis performed based on the data in Table 3.
Table 3: Data on the nights spent by tourists from Japan and amount spent
Year
Average no. of nights spent
Average amount spent (in RM billion)
2010
5.9
1.1
2011
6.1
1.1
2012
6.1
1.4
2013
6.3
1.5
2014
6.4
1.8
2015
6.1
1.6
2016
6.2
1.3
2017
6.3
1.2
2018
6.6
1.7
2019
6.9
2.3
Table 4: Regression analysis
Coefficients
Standard Error
t Stat
P-value
Intercept
B0
1.4555
-3.7583
0.0056
Average no. of nights spent
B1
0.2312
4.7934
0.0014
a. Note that the value of B0 and B1 are missing from Table 4.…
3. (a). Differentiate the different types of linear regression and describe the use of regression in geographical study.
(b). Calculate the value of the slope, b, for observations of n = 22, r2 = 0.73, standard deviation of x = 2.3 and the regression sum of square = 1324.
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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_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardAn article on estimating 28-day strength of concrete considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = = 1,750 + 1.5x. (a) What is the expected value (in pounds per square inch) of 28-day strength when accelerated strength = 2,490 psi? psi (b) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength increases by 1 psi? psi (c) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength increases by 50 psi? psi (d) By how much can we expect 28-day strength (in pounds per square inch) to change when accelerated strength decreases by 50 psi? psiarrow_forward
- Suppose a study wants to predict the market price of a certain species of turtle (Y) based on the following independent variables indicated in the table. Based from the table, what is the equation of the multiple linear regression? (Round off up to two decimal places. Market Price = 0.07 - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 + 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 - 0.40 + weight + 1.51 + length + 1.41 + width + 0.80 + agearrow_forwardState in algebraic notation and explain the assumption about the classical linear regression models disturbances that are referred to by the term ‘homoscedasticity’.arrow_forwardSuppose you are estimating a wage regression, where salary is the dependent variable and age, years of education and a dummy variable for male are your independent variables. You are interested in measuring how salary differs between those who have at least a college education with those who have less than a college education. If a person is considered as having a college education when she has more than 12 years of education, how can you measure the difference in salary between college and non-college educated individuals? Select one: a. Multiply coefficient for years of education in original regression by 12 O b. Re-estimate model replacing years of education with a dummy variable for college c. Re-estimate model replacing years of education with a dummy variable for college and one for no college O d. Re-estimate model interacting years of education with a dummy variable for college e. Calculate the difference in predicted salary between an individual with 14 years of education and…arrow_forward
- A student is preparing to take a standardized exam. She was told that she needs to get plenty of sleep the night before the exam. She is interested in the relationship between the number of hours of sleep a student gets before the exam and the score earned on the exam. She collects information from 10 other students who have already taken the exam as shown in the table. Based on the residual plot, is the linear model appropriate? No, there is no clear pattern in the residual plot. Yes, there is no clear pattern in the residual plot. No, the student who got the most sleep had a negative residual. Yes, there are more negative residuals (6) than positive residuals (4).arrow_forwardIf an estimated regression line has a y-intercept of 10 and a slope of -4, then when x= 2, the predicted value of y is?arrow_forwardA 1 Demand 2 WN 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 7.38 8.51 9.52 7.50 9.33 8.28 8.75 7.87 7.10 8.00 7.89 8.15 9.10 8.86 8.90 8.87 9.26 9.00 8.75 7.95 7.65 7.27 8.00 8.50 8.75 9.21 8.27 7.67 7.93 9.26 B PriceDif -0.05 0.25 0.60 0.00 0.25 0.20 0.15 0.05 -0.15 0.15 0.20 0.10 0.40 0.45 0.35 0.30 0.50 0.50 0.40 -0.05 -0.05 -0.10 0.20 0.10 0.50 0.60 -0.05 0.00 0.05 0.55 Carrow_forward
- 3. Suppose you want to analyse personal consumption expenditures by using income. However, you also believe that personal consumption expenditures might vary by gender (female-male) and marital status (married-single). (a) By setting appropriate dummy variables, construct a regression where not only the autonomous consumption but also the marginal propensity to consume are allowed to vary by gender and marital status. In your regression, you should have the assumption that the 3 differential effect of gender (marital status) on autonomous consumption and marginal propensity to consume is the same across two categories of marital status (gender). Once you construct your regression, derive the expected personal consumption expenditures of each group. (b) Re-construct the regression in (a) by allowing the differential effect of gender (marital status) on autonomous consumption and marginal propensity to consume to vary across two categories of marital status (gender) and derive expected…arrow_forwardb) pleasearrow_forwardNonearrow_forward
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