Is there a relationship between the sodium content of a hot dog and the number of calories the hot dog has? To investigate this, a nutritionist randomly picked n= 51 hot dog wieners all of which were the same size. For each hot dog wiener the sodium content (in milligrams) was measured and the number of calories each contained, after cooking The nutritionist wants to estimate the statistical model Y, - A + PX, + e where Y, represents the caloric content, or the number of calories, of hot dog wiener i, and X, represents the sodium content (n milligrams) of hot dog wiener i. The data appears in the .csv file. Open this file, then copy-and-paste the columns into the statistical software. (a) Using the statistical software, graph the bivariate data. What can you say about nature of the relationship between the sodium content of a hotdog wiener and the caloric content of the hot dog wiener? There is exists a ? v relationship between the sodium content of a hotdog wiener and its caloric content. (b) Compute the correlation between a hot dog wieners sodium and caloric content. II une four decimals in your answer) (c) Fill in the blanks to estimate the statistical model. For each field, use three decimals. 目 X. (d) A residual plot appears below Residual Plot 300 Ped w Y This residual plot is use to check the condition of ? . This condtion ? appear to hold. (e) What percent of the variation in the caloric content of a hot dog wiener is explained by its linear relationship with its sodium content? Enter your answer as a %. % (use two decimals)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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R-Studio or by hand is fine. Thanks in advance! The following is the data:

 

sodium

calories

1

129

317

2

180

555

3

117

265

4

142

369

5

164

523

6

153

391

7

140

394

8

143

472

9

143

501

10

167

434

11

117

382

12

140

379

13

158

415

14

135

417

15

130

350

16

210

617

17

149

505

18

161

506

19

132

342

20

122

446

21

161

454

22

166

496

23

102

317

24

119

400

25

112

400

26

207

636

27

183

587

28

151

463

29

152

524

30

178

381

31

96

441

32

176

518

33

163

561

34

145

375

35

196

530

36

114

334

37

179

433

38

160

407

39

160

583

40

156

377

41

92

265

42

145

268

43

148

422

44

122

412

45

204

509

46

108

310

47

116

256

48

138

496

49

91

326

50

155

507

51

173

567

Is there a relationship between the sodium content of a hot dog and the number of calories the hot dog has? To investigate this, a nutritionist randomly picked n = 51 hot dog wieners all of which were the same size. For each hot dog wiener the sodium content (in milligrams) was measured and the number of calories each contained, after cooking.
The nutritionist wants to estimate the statistical model
Y; = fo + B1 X; + e;
where Y; represents the caloric content, or the number of calories, of hot dog wiener i, and X; represents the sodium content (in milligrams) of hot dog wiener i.
The data appears in the .csv file. Open this file, then copy-and-paste the columns into the statistical software.
(a) Using the statistical software, graph the bivariate data. What can you say about nature of the relationship between the sodium content of a hotdog wiener and the caloric content of the hot dog wiener?
There is exists a
?
v relationship between the sodium content of a hotdog wiener and its caloric content.
(b) Compute the correlation between a hot dog wieners sodium and caloric content.
r =
(use four decimals in your answer)
(c) Fill in the blanks to estimate the statistical model. For each field, use three decimals.
? v
X;
(d) A residual plot appears below
Residual Plot
300
350
400
450
500
550
Predicted Values of Y
This residual plot is use to check the condition of ?
V. This condition ?
appear to hold.
(e) What percent of the variation in the caloric content of a hot dog wiener is explained by its linear relationship with its sodium content? Enter your answer as a %.
% (use two decimals)
09
0s-
00-
Residuals
Transcribed Image Text:Is there a relationship between the sodium content of a hot dog and the number of calories the hot dog has? To investigate this, a nutritionist randomly picked n = 51 hot dog wieners all of which were the same size. For each hot dog wiener the sodium content (in milligrams) was measured and the number of calories each contained, after cooking. The nutritionist wants to estimate the statistical model Y; = fo + B1 X; + e; where Y; represents the caloric content, or the number of calories, of hot dog wiener i, and X; represents the sodium content (in milligrams) of hot dog wiener i. The data appears in the .csv file. Open this file, then copy-and-paste the columns into the statistical software. (a) Using the statistical software, graph the bivariate data. What can you say about nature of the relationship between the sodium content of a hotdog wiener and the caloric content of the hot dog wiener? There is exists a ? v relationship between the sodium content of a hotdog wiener and its caloric content. (b) Compute the correlation between a hot dog wieners sodium and caloric content. r = (use four decimals in your answer) (c) Fill in the blanks to estimate the statistical model. For each field, use three decimals. ? v X; (d) A residual plot appears below Residual Plot 300 350 400 450 500 550 Predicted Values of Y This residual plot is use to check the condition of ? V. This condition ? appear to hold. (e) What percent of the variation in the caloric content of a hot dog wiener is explained by its linear relationship with its sodium content? Enter your answer as a %. % (use two decimals) 09 0s- 00- Residuals
(f) Does the data support the statistical model? Select the appropriate statistical hypotheses.
A. Ho : B1 = 0 HẠ : B1 + 0
В. Но : В 3D 0 На : В > 0
С. Но : Во 3 0 На : Во > 0
D. Ho : Bo = 0 HẠ : Bo + 0
E. Ho : B1 > 0 HẠ : B1 = 0
F. H, : Bo = 0 HẠ : Bo < 0
G. Но : В 3D 0 На : В <0
||
(g) Find the value of the test statistic that is based on the random behaviour of ß1, and the P-value that is used to test the null hypothesis in part (f) .
Test Statistic
(Use three decimals in your answer)
Р- value 3D
(Use SIX decimals in your answer)
(h) Complete the statement below. In doing so, use three decimals in your answers.
I am 95% confidence that as the sodium content of a hot dog wiener increases by 1 milligram, the mean carolic content of the hot dog wiener will ?
by somewhere between
calories and
calories.
(i) A particular hot dog wiener has 114 milligrams of sodium. With 95% confidence, estimate the mean carolic content of all hot dog wieners that have 114 milligrams of sodium.Use one decimal in your answers.
< HY|X=114 <|
Transcribed Image Text:(f) Does the data support the statistical model? Select the appropriate statistical hypotheses. A. Ho : B1 = 0 HẠ : B1 + 0 В. Но : В 3D 0 На : В > 0 С. Но : Во 3 0 На : Во > 0 D. Ho : Bo = 0 HẠ : Bo + 0 E. Ho : B1 > 0 HẠ : B1 = 0 F. H, : Bo = 0 HẠ : Bo < 0 G. Но : В 3D 0 На : В <0 || (g) Find the value of the test statistic that is based on the random behaviour of ß1, and the P-value that is used to test the null hypothesis in part (f) . Test Statistic (Use three decimals in your answer) Р- value 3D (Use SIX decimals in your answer) (h) Complete the statement below. In doing so, use three decimals in your answers. I am 95% confidence that as the sodium content of a hot dog wiener increases by 1 milligram, the mean carolic content of the hot dog wiener will ? by somewhere between calories and calories. (i) A particular hot dog wiener has 114 milligrams of sodium. With 95% confidence, estimate the mean carolic content of all hot dog wieners that have 114 milligrams of sodium.Use one decimal in your answers. < HY|X=114 <|
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