Question

Data on the fuel consumption yy of a car at various speeds xx is given. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least‑squares regression line is^y=55.3286−0.02286xy^=55.3286−0.02286xUsing this equation, we can add the residuals to the original data.

Speed | 1010 | 2020 | 3030 | 4040 | 5050 | 6060 | 7070 | 8080 |
---|---|---|---|---|---|---|---|---|

Fuel | 38.138.1 | 54.054.0 | 68.468.4 | 63.663.6 | 60.560.5 | 55.455.4 | 50.650.6 | 43.843.8 |

Residual | −17.00−17.00 | −0.87−0.87 | 13.7613.76 | 9.199.19 | 6.316.31 | 1.441.44 | −3.13−3.13 | −9.70−9.70 |

To access the complete data set, click the link for your preferred software format:

Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt!

(a) Use the software of your choice to make a scatterplot of the observations. Have the software include the regression line on the plot, or print the scatterplot and draw the regression line provided on your plot.

(b) Would you use the regression line to predict yy from x?x?

No, the pattern is a straight line, so linear regression is not appropriate for prediction.

Yes, the pattern is a straight line, so linear regression is appropriate for prediction.

Yes, the pattern is nonlinear, so linear regression is appropriate for prediction.

No, the pattern is nonlinear, so linear regression is not appropriate for prediction.

(c) On a separate sheet of paper, verify the value of the first residual, for x=10.x=10. Then verify that the residuals add up to 0.0.

(d) Now use the residuals and x-valuesx-values in the table to make a plot of the residuals against the values of x,x, also on a separate sheet of paper. Draw a horizontal line at height 00 on your plot.

Compare your scatter plot with your regression plot. How does the pattern of the residuals about this line compare with the pattern of the data points about the regression line in your original scatterplot?

The observations in the scatter plot that are above the regression line have

and the observations in the scatter plot that are below the regression line have

The distance of the observations above the regression line is

the value of the residual, and the distance of the observations below the regression line is

the absolute value of the residual. Therefore, the pattern of the residuals is

the pattern of the data points about the regression line in the original scatterplot.

Answer #1

Bone mineral density and cola consumption has been recorded for
a sample of patients. Let xx represent the number of colas consumed
per week and yy the bone mineral density in grams per cubic
centimeter. Based on the data shown below answer the questions
rounding your final answers to four decimal places.
(a) Create a scatter plot with linear regression line for the data.
(2 points)
y = x +
(b) Interpret the slope of the regression equation in a complete...

The Great Lakes Auto Maker is interested in studying how fuel
consumption is related to the number of tests for the engines for
its cars on a certain route between Grand Rapids and Detroit. A
random sample of 10 cars on this route has yielded the data in the
table below. Do parts (A), (B) and C
No. Test Engine
Units/Limits
22
48
25
52
37
91
31
80
47
114
43
98
39
87
50
122
40
100
29...

Find the equation of the regression line for the given data.
Then construct a scatter plot of the data and draw the regression
line. (Each pair of variables has a significant correlation.)
Then use the regression equation to predict the value of y for each
of the given x-values, if meaningful. The caloric content and the
sodium content (in milligrams) for 6 beef hot dogs are shown in
the table below.
Calories, x Sodium, y
150 420
170 470...

1. Given the following observations of quantitative variables
X and Y:
x= 0, 1, 2, 3, 15
y= 3, 4, 6, 10, 0
a. Make a scatterplot of the data on the axes. Circle the most
influential observation. (4 points)
(b) Determine the LSRL of Y on X. Draw
this line carefully on your scatterplot. (4 points)
(c) What is the definition of a regression outlier? (4
points)
(d) Which data point is the biggest regression outlier?
(4 points)...

The data table found below contains the listed prices and
weights of the diamonds in 20 rings offered for sale in a newspaper
in a foreign city. The prices are in local dollars with the weights
in carats. Complete parts (a) through (g) below.
Weight (carats)
Price (dollars)
0.13
224
0.22
578
0.24
649
0.12
229
0.3
895
0.38
1155
0.24
624
0.28
781
0.14
270
0.25
628
0.21
514
0.14
275
0.25
640
0.39
1239
0.3
831
0.12
191...

A statistical program is recommended.
Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized...

Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized residual with the largest absolute...

The following data were used in a regression study.
Observation
1
2
3
4
5
6
7
8
9
xi
2
3
4
5
7
7
7
8
9
yi
3
5
4
7
4
6
9
4
11
(a)
Develop an estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ =
(b)
Construct a plot of the residuals.
A residual plot has 9 points plotted on it. The horizontal axis
ranges from 0...

xi
6
11
15
18
20
yi
5
8
12
20
30
(a)
Develop an estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ =
(b)
Compute the residuals. (Round your answers to two decimal
places.)
xi
yi
Residuals
6
5
11
8
15
12
18
20
20
30
(c)
Develop a plot of the residuals against the independent variable
x.
A residual plot has 5 points plotted on it. The horizontal axis
ranges...

Here is the data Stat7_prob3.txt :
"FATALS","CUTTING"
270,15692
183,16198
319,17235
103,18463
149,18959
124,19103
62,19618
298,20436
330,21229
486,18660
302,17551
373,17466
187,17388
347,15261
168,14731
234,14237
68,13216
162,12017
27,11845
40,11905
26,11881
41,11974
116,11892
84,11810
43,12076
292,12342
89,12608
148,13049
166,11656
32,13305
72,13390
27,13625
154,13865
44,14445
3,14424
3,14315
153,13761
11,12471
9,10960
17,9218
2,9054
5,9218
63,8817
41,7744
10,6907
3,6440
26,6021
52,5561
31,5309
3,5320
19,4784
10,4311
12,3663
88,3060
0,2779
41,2623
2,2058
5,1890
2,1535
0,1515
0,1595
23,1803
4,1495
0,1432
Here is the question :
Please Use R software/studio...

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