Elementary Statistics
12th Edition
ISBN: 9780321836960
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 10.5, Problem 17BB
To determine
To test: The claim that
To explain: The results imply about the regression equation.
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Bivariate data obtained for the paired variablesx and y are shown below, in the table labelled "Sample data." These data
are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation
for this line is y =-4.87+1.06x .
In the "Calculations" tabl : calculations involving the observed y values, the mean y of these values, and the values
y predicted from the regression equation.
Sample data
Calculations
團
160+
6-7 G-7) G-
х
150+
111.4 115.6
318.9796
409.9005
5.6930
140
122.2 121.5
143.0416
77.4048
9.9982
132.0 139.8
40.1956
2.5281
22.5625
130+
138.6 130.1
11.2896
73.7194
142.7069
120-
151.1 160.3
720.3856
476.8109
25.0400
110-
Column
1233.8920
1040.3637
206.0007
sums
110
120
130
140
150
160
Send data to Excel
Figure 1
Answer the following:
1. The variation in the sample y values that is not explained by the estimated linear
relationship between x and y is given by the ?
v, which for these
data is ?
2. The value r is the…
Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure
1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87+0.88x.
In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression
equation.
Sample data
Calculations
160+
x
y
(x-1)²
(-5)²
(v-^^)²
150+
107.2 110.7
396.0100
457.7032
2.2320
122.0 130.3
140-
0.0900
70.0569
65.1249
131.5 122.1
130-
72.2500
0.0001
72.0801
142.5 129.9
120.
0.4900
93.5089
107.5369
152.5 160.0
110-
864.3600
341.1409
119.4649
Send data to Excel
LL
130 130 140 150 160
Column sum:
1333.2000
Column sum:
962.4100
Column sum:
366.4388
Figure 1
Answer the following.
(a)
The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best
fits" is used because the line has an…
How the most common use of a one-sided t-test is to determine whether a regression coefficient ?
Chapter 10 Solutions
Elementary Statistics
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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_forwardObservations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars). X₁ = display floor space (square meters), X₂= competitors' advertising expenditures (thousands of dollars), X₁ = advertised price (dollars per unit). Predictor Intercept FloorSpace CompetingAds Price Coefficient 1,243.88 13.74 -6.848 -0.1461 (a) Write the fitted regression equation. (Round your coefficient CompetingAds to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) *FloorSpace+ *CompetingAds+ (b-1) The coefficient of FloorSpace says that each additional square foot of floor space O takes away 13.74 from sales (in thousands of dollars) O adds about 13.74 to sales (in thousands of dollars) adds about 6.848 to sales (in thousands of dollars) takes away 01496 from sales (in thousands of dollars) (b-2) The coefficient of CompetingAds…arrow_forwardA researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 2000 for each of the 52 cities randomly selected in the US. As part of his study, he ran the following simple linear regression model: Ho:B1=0 versus H1:B1 not equal =/ to 0. Based on the results from table in photo, determine the value of correlation Rsquared of this simple linear regression model. Help me understand how you solved for R-squared.arrow_forward
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