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)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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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

(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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Calculus For The Life Sciences

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