Question

In: Statistics and Probability

Problem You will complete a question about Correlation Examples and complete a Simple Linear Regression. For...

Problem
You will complete a question about Correlation Examples and complete a Simple Linear Regression. For the Simple Linear Regression, make sure to complete the following steps:

Construct a scatter plot.
Find the equation of the regression line.
Predict the value of y for each of the x-values.
Use this resource: Regression

Give an example of two variables that have a positive linear correlation. Give an example of two variables that have a negative linear correlation. Give an example of two variables that have no correlation.
Protein and Fat: The protein (in grams) and fat (in grams) of eleven health foods are shown in this table

Protein, x	20	22	23	26	26	27	28	30	31	33	33
Fat, y	18	20	19	18	16	17	17	15	16	14	14

x = 21 grams
x = 25 grams
x = 32 grams

Expert Solution

X

y

(x-xbar)^2

(x-xbar)(y-ybar)

20
22
23
26
26
27
28
30
31
33
33

18
20
19
18
16
17
17
15
16
14
14

51.579
26.851
17.488
1.397
1.397
0.033
0.669
7.942
14.579
33.851
33.851

Sum: 189.636

-9.140
-16.959
-9.504
-1.504
0.860
-0.050
0.223
-4.868
-2.777
-15.868
-15.868

Sum: -75.455

B) regression equation

Sum of X = 299
Sum of Y = 184
Mean X = 27.1818
Mean Y = 16.7273
Sum of squares (SS_X) = 189.6364
Sum of products (SP) = -75.4545

Regression Equation = ŷ = bX + a

b = SP/SS_X = -75.45/189.64 = -0.39789

a = M_Y - bM_X = 16.73 - (-0.4*27.18) = 27.54267

ŷ = -0.39789X + 27.54267

Predicted value

orchestra answered 2 years ago

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