STAT 180 Statistics Project Carbohydrate Content and Calorie Levels

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Mathematics

STAT 180

Description

Part 1 ; Identify a group of points that represent a subgroup of menu items

(for example the salads, or dessets, etc.) from your original data, and separate them as a

distinct smaller data set. Then create new scatterplots with regression equation, r, and R2,for both the new group and the remaining group of data. Compare those two models to

each other and to the original full data set model, explaining how they are different,

interpreting the new equations, and explaining why they would be different. Finally, decide

which model is the better predicter if they are appreciably different. Expected length: 1-2

pages of writing; in other words, there should also be scatterplots that don’t count in the

length.

Part 2 ; Identify an outlier or high leverage point (or two or three) and

eliminate it from your data set. Then create a new scatterplot, and recalculate your

regression equation, r, and R2

, using the remaining data points. Compare the new results to

your original results. Explain how they are different, interpret the new equation, and

explain why they would be different. Finally, decide which model is the better predicter if

they are appreciably different. Expected length: 1-2 pages of writing; in other words, there

should also be scatterplots that don’t count in the length.

Unformatted Attachment Preview

TITLE Correlation Between Carbohydrate Content and Calorie Levels in Hardees' Food Calories (x) 3pc Hand Breaded Chicken Tenders Beef Super Nachos Big Chicken Filet Sandwich Charbroiled Chicken Club Sandwich Charbroild BBQ Chicken Sandwich Big Hot Ham N Cheese Spicy Chicken Sandwich Chicken Taco Salad Southern-Style Tender sandwich Beef Taco Salad Chicken Super Nachos Medium Natural-Cut French Fries Red Burrito Chicken Bowl Steak Bowl Crispy Curls (medium) 1/3lb Original Thickburger Chocolate Chip cookies Side Salad Beer-battered onion rings Apple turnover Low Carb It Charbroiled Chicken Club sandwich Low Carb It Thickburger Beef Grilled Burrito Chicken Grilled Burrito Beef Soft Taco Chicken Soft Taco Beef Taco Steak Quesadilla Frisco Thickburger Chicken Quesadilla Carbohydrates (y) 260 560 710 560 350 530 440 960 530 920 580 490 430 450 470 780 290 120 410 270 340 470 700 630 210 230 180 910 840 640 Predicted y^ 13 57 64 38 46 51 21 74 58 72 58 63 55 55 60 56 35 45 45 35 13 9 71 70 17 18 13 81 46 43 r= R^2 = 0.725143015 0.525832392 x bar mean of x y bar mean of y 508.6666667 46.06666667 29.608 49.468 59.398 49.468 35.566 47.482 41.524 75.948 47.482 73.3 50.792 44.834 40.862 42.186 43.51 64.032 31.594 20.34 39.538 30.27 34.904 43.51 58.736 54.102 26.298 27.622 24.312 72.638 68.004 54.764 evels in Hardees' Food Residuals (y-y^) -16.608 7.532 4.602 -11.468 10.434 3.518 -20.524 -1.948 10.518 -1.3 7.208 18.166 14.138 12.814 16.49 -8.032 3.406 24.66 5.462 4.73 -21.904 -34.51 12.264 15.898 -9.298 -9.622 -11.312 8.362 -22.004 -11.764 Residuals Plot 30 Carbohydrates 20 0 0 5 10 15 -10 -20 -30 -40 Calories Regression of Carbohydrates (y 90 80 Carbohydrates 70 60 50 40 30 20 10 0 0 0.0662 slope, b1 = 12.396 intercept, b0 = Sx = Sy = 10 228.287981 20.8391762 200 400 Residuals Plot 15 20 25 30 35 Calories ion of Carbohydrates (y) on Calories (x) y = 0.0662x + 12.396 R² = 0.5258 600 Calories 800 1000 1200
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Explanation & Answer

Attached.

TITLE

Correlation Between Carbohydrate Content and Calorie Level
Calories (x)

3pc Hand Breaded Chicken Tenders
Beef Super Nachos
Big Chicken Filet Sandwich
Charbroiled Chicken Club Sandwich
Charbroild BBQ Chicken Sandwich
Big Hot Ham N Cheese
Spicy Chicken Sandwich
Chicken Taco Salad
Southern-Style Tender sandwich
Beef Taco Salad
Chicken Super Nachos
Medium Natural-Cut French Fries
Red Burrito Chicken Bowl
Steak Bowl
Crispy Curls (medium)
1/3lb Original Thickburger
Chocolate Chip cookies
Side Salad
Beer-battered onion rings
Apple turnover
Low Carb It Charbroiled Chicken Club sandwich
Low Carb It Thickburger
Beef Grilled Burrito
Chicken Grilled Burrito
Beef Soft Taco
Chicken Soft Taco
Beef Taco
Steak Quesadilla
Frisco Thickburger
Chicken Quesadilla

Carbohydrates (y)
260
560
710
560
350
530
440
960
530
920
580
490
430
450
470
780
290
120
410
270
340
470
700
630
210
230
180
910
840
640

13
57
64
38
46
51
21
74
58
72
58
63
55
55
60
56
35
45
45
35
13
9
71
70
17
18
13
81
46
43

r=
R^2 =

0.725143015
0.525832392

x bar mean of x
y bar mean of y

508.6666667
46.06666667

Content and Calorie Levels in Hardees' Food
Residuals (y-y^)
-16.608
7.532
4.602
-11.468
10.434
3.518
-20.524
-1.948
10.518
-1.3
7.208
18.166
14.138
12.814
16.49
-8.032
3.406
24.66
5.462
4.73
-21.904
-34.51
12.264
15.898
-9.298
-9.622
-11.312
8.362
-22.004
-11.764

30
20

Carbohydrates

29.608
49.468
59.398
49.468
35.566
47.482
41.524
75.948
47.482
73.3
50.792
44.834
40.862
42.186
43.51
64.032
31.594
20.34
39.538
30.27
34.904
43.51
58.736
54.102
26.298
27.622
24.312
72.638
68.004
54.764

0
0
-10
-20

-40

90
80
70
60
50
40
30
20
10
0
0

0.0662 slope, b1 =
12.396 intercept, b0 =
Sx =
Sy =

10

-30

Carbohydrates

Predicted y^

228.28798
20.8391762

Residuals Plot
30
20
10
0
0

5

10

15

20

25

30

35

-10
-20
-30
-40

Calories

Regression of Carbohydrates (y) on Calories (x)

y = 0.0662x + 12.396
R² = 0.5258

0

200

400

600

Calories

800

1000

1200

TITLE
Remaining Group of Data

Correlation Between Carbohydrate Content and Calorie Levels in

3pc Hand Breaded Chicken Tenders
Beef Super Nachos
Big Chicken Filet Sandwich
Charbroiled Chicken Club Sandwich
Charbroild BBQ Chicken Sandwich
Big Hot Ham N Cheese
Spicy Chicken Sandwich
Southern-Style Tender sandwich
Chicken Super Nachos
Medium Natural-Cut French Fries
Red Burrito Chicken Bowl
Steak Bowl
Crispy Curls (medium)
1/3lb Original Thickburger
Chocolate Chip cookies
Apple turnover
Low Carb It Charbroiled Chicken Club sandwich
Low Carb It Thickburger
Beef Grilled Burrito
Chicken Grilled Burrito
Beef Soft Taco
Chicken Soft Taco
Beef Taco
Frisco Thickburger
Chicken Quesadilla
Steak Quesadilla
Beer-battered onion rings

90
C
a
r
b
o
h
y
d
a
r
t
e

80
70
60
50
40
30
20
10

Calories (x)Carbohydrates (y)
260
13
560
57
710
64
560
38
350
46...


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