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CalibriB11ABDFW3EFW4FGBarefoot FW1w234.851 32.927237.455 31.719 27.937 27.48320.68732.62621.33628.22921.74930.88937.56514.57317.30930.92118.468 11.617 23.863 26.681332.61623.067 28.61426.665 26.05624.865 28.931431.5937.228 27.90823.782 23.766 25.293524.749 24.80931.21823.64 37.264 27.016 27.615 29.04427.416 30.716 22.181 27.281 31.01620.052 17.486 11.29620.186630.97822.463 25.386791018.07920.90919.65932.87512.859 16.772 16.28923.155 24.625 18.36321.6621.80827.784 20.623 21.23321.5430.7251117.60920.36928.188 28.678 29.01322.50129.01312.07 14.428 24.30824.325 31.178 22.12125.89327.762 25.49820.58627.119 26.50912131415161731.30125.89419.964 23.087 25.47524.9730.30527.3520.38726.95333.15323.463 33.4533.77 28.26324.0151821.203 25.03323.8622.761 26.053 29.894 23.95420.40223.43420.32120.32521.877 20.653 26.294 26.09317 I6డి ఎ3.874 7 రీతర)1926.065 34.13316.658 27.80530.123 28.4142015.032 26.853 27.77827.457 26.625 27.53915.2 33.39519.357212215.447 22.07323.924 25.47813.807 24,11216.11422.7డ0.700 20.33423242516.36529.161 30. 178 25.869 31.88412.1272627 22.53323.005 18.48719.14ட9.155 21.793 20111 1214)29Sheet i

Question

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion.

 

In particular, note the variables Barefoot and Footwear1. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear1 represents their range of ankle motion (in degrees) while wearing typical shoes.

Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing typical shoes, y^ , based on their range of ankle motion while barefoot, x . Round your coefficients to two decimal places of precision.

?̂ =
 
 
A physical therapist determines that her patient Jan has a range of ankle motion of 7.26° while barefoot. Predict Jan's range of ankle motion while wearing typical shoes, ?̂  . Round your answer to two decimal places.
?̂ =
 
°
Suppose Jan's actual range of ankle motion while wearing typical shoes is 9.79° . Use her predicted range of ankle motion to calculate the residual associated with this value. Round your answer to two decimal places.
residual=
 
°

In order to assess the linear regression equation's ability to predict range of ankle motion, the physical therapist reviewed a scatterplot of the researchers' sample data and calculated the correlation, r=0.64 .

Calibri
B
11
A
B
D
FW3
E
FW4
F
G
Barefoot FW1
w2
34.851 32.927
2
37.455 31.719 27.937 27.483
20.687
32.626
21.336
28.229
21.749
30.889
37.565
14.573
17.309
30.921
18.468 11.617 23.863 26.681
3
32.616
23.067 28.614
26.665 26.056
24.865 28.931
4
31.59
37.228 27.908
23.782 23.766 25.293
5
24.749 24.809
31.218
23.64 37.264 27.016 27.615 29.044
27.416 30.716 22.181 27.281 31.016
20.052 17.486 11.296
20.186
6
30.978
22.463 25.386
7
9
10
18.079
20.909
19.659
32.875
12.859 16.772 16.289
23.155 24.625 18.363
21.66
21.808
27.784 20.623 21.233
21.54
30.725
11
17.609
20.369
28.188 28.678 29.013
22.501
29.013
12.07 14.428 24.308
24.325 31.178 22.121
25.89327.762 25.498
20.586
27.119 26.509
12
13
14
15
16
17
31.301
25.894
19.964 23.087 25.475
24.97
30.305
27.35
20.387
26.953
33.153
23.463 33.45
33.77 28.263
24.015
18
21.203 25.033
23.86
22.761 26.053 29.894 23.954
20.402
23.434
20.321
20.325
21.877 20.653 26.294 26.093
17 I6డి ఎ3.874 7 రీతర)
19
26.065 34.133
16.658 27.805
30.123 28.414
20
15.032 26.853 27.778
27.457 26.625 27.539
15.2 33.395
19.357
21
22
15.447 22.073
23.924 25.478
13.807 24,112
16.114
22.7
డ0.700 20.334
23
24
25
16.365
29.161 30. 178 25.869 31.884
12.127
26
27 22.533
23.005 18.487
19.14
ட9.155 21.793 20111 1214)
29
Sheet i
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Image Transcriptionclose

Calibri B 11 A B D FW3 E FW4 F G Barefoot FW1 w2 34.851 32.927 2 37.455 31.719 27.937 27.483 20.687 32.626 21.336 28.229 21.749 30.889 37.565 14.573 17.309 30.921 18.468 11.617 23.863 26.681 3 32.616 23.067 28.614 26.665 26.056 24.865 28.931 4 31.59 37.228 27.908 23.782 23.766 25.293 5 24.749 24.809 31.218 23.64 37.264 27.016 27.615 29.044 27.416 30.716 22.181 27.281 31.016 20.052 17.486 11.296 20.186 6 30.978 22.463 25.386 7 9 10 18.079 20.909 19.659 32.875 12.859 16.772 16.289 23.155 24.625 18.363 21.66 21.808 27.784 20.623 21.233 21.54 30.725 11 17.609 20.369 28.188 28.678 29.013 22.501 29.013 12.07 14.428 24.308 24.325 31.178 22.121 25.89327.762 25.498 20.586 27.119 26.509 12 13 14 15 16 17 31.301 25.894 19.964 23.087 25.475 24.97 30.305 27.35 20.387 26.953 33.153 23.463 33.45 33.77 28.263 24.015 18 21.203 25.033 23.86 22.761 26.053 29.894 23.954 20.402 23.434 20.321 20.325 21.877 20.653 26.294 26.093 17 I6డి ఎ3.874 7 రీతర) 19 26.065 34.133 16.658 27.805 30.123 28.414 20 15.032 26.853 27.778 27.457 26.625 27.539 15.2 33.395 19.357 21 22 15.447 22.073 23.924 25.478 13.807 24,112 16.114 22.7 డ0.700 20.334 23 24 25 16.365 29.161 30. 178 25.869 31.884 12.127 26 27 22.533 23.005 18.487 19.14 ட9.155 21.793 20111 1214) 29 Sheet i

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check_circleAnswer
Step 1

Introduction:

Here, the response variable, y, is the range of ankle motion while wearing typical shoes. The values of this variable are given in the column “FW1”.

The predictor variable, x is the range of ankle motion while barefoot. The values of this variable are given in the column “Barefoot”.

Step 2

Calculation:

The regression analysis can be performed using Excel.

Consider the data entered as in the image you have provided. Rename the first column, that is, the column named Barefoot as x, and the second column, that is, the column named FW1 as y, for convenience.

Go to Data > Data Analysis (an Excel in-built...

SUMMARY OUTPUT
Regression Statistics
0.636463337
Multiple R
0.40508558
R Square
Adjusted R Square 0.381289003
Standard Error
4.467993588
Observations
27
ANOVA
df
Significance F
SS
MS
Regression
339.8266064 339.8266064 17.02285093 0.000358375
Residual
25
499.0741676 19.96296671
Total
838.900774
26
Coefficients Standard Error
Upper 95%
Lower 95.0 % Upper 95.0 %
Lower 95%
t Stat
Pvolue
Intercept
11.67882575
3.649428827 3.200179071 0.003714338 4.162686388 19.19496512 4.162686388 19.19496512
0.634747977
0.153845635 4.125875778 0.000358375 0.317896962 0.951598993 0.317896962 0.9515s98993
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Image Transcriptionclose

SUMMARY OUTPUT Regression Statistics 0.636463337 Multiple R 0.40508558 R Square Adjusted R Square 0.381289003 Standard Error 4.467993588 Observations 27 ANOVA df Significance F SS MS Regression 339.8266064 339.8266064 17.02285093 0.000358375 Residual 25 499.0741676 19.96296671 Total 838.900774 26 Coefficients Standard Error Upper 95% Lower 95.0 % Upper 95.0 % Lower 95% t Stat Pvolue Intercept 11.67882575 3.649428827 3.200179071 0.003714338 4.162686388 19.19496512 4.162686388 19.19496512 0.634747977 0.153845635 4.125875778 0.000358375 0.317896962 0.951598993 0.317896962 0.9515s98993

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