Use the “CropYield” dataset for this problem. The y-variable is Yield = the yield of a crop during...

Question

Use the “CropYield” dataset for this problem. The
y-variable is Yield = the yield of a crop during a growing season. There are two
x-variables. The variable IngredA = the amount of ingredient A put into a soil treatment used to help grow the crop and the variable IngredB = the amount of ingredient B put into a soil treatment. Twelve combinations of IngredA (which had 3 different levels) and IngredB (which had 4 different levels) were considered. Two fields were treated with each combinations so the sample size of the dataset is
n
= 24.

Using statistical software, plot IngredA versus IngredB. This is a plot of the two
x-variables. On the basis of this plot, describe in words the amount of correlation between the two
x-variables?

Now, graph Yield versus IngredA and separately graph Yield versus IngredB. Describe the important features of each plot. For instance, are the relationships linear, are there any outliers, which
x-variable is the stronger predictor, and so on?

Fit a simple linear regression model with
y
= Yield and
x
= IngredA.
1. What is the value of the slope? Write a sentence that interprets this slope.
2. What is the value of
  R
  ²
  for this regression?
3. On the basis of this regression, can we say that there is a statistically significant linear relationship between Yield and IngredA? Explain why or why not.

Fit a simple linear regression model with
y
= Yield and
x
= IngredB.
1. What is the value of the slope? Write a sentence that interprets this slope.
2. What is the value of
  R
  ²
  for this regression?
3. On the basis of this regression, can we say that there is a statistically significant linear relationship between Yield and IngredB? Explain why or why not.

Fit a multiple linear regression model with
y
= Yield using predictors
x
₁
= IngredA and
x
₂
= IngredB.
1. What are the values of the coefficients that multiply the two
  x-variables? Explain why these are the same values found in the previous two parts of this question.
2. What is the value of
  R
  ²
  for this regression? Verify that this
  R
  ²
  is the sum of the
  R
  ²
  values for the simple regressions done in the previous two parts of this question, and explain why this relationship holds here.
3. On the basis of this regression, can we say that there is a statistically significant relationship between Yield and IngredA? Explain why or why not.

DATA:
IngredA IngredB Yield
1 1 22.6
1 2 30.9
1 3 31.5
1 4 35.6
2 1 24.4
2 2 32.3
2 3 34
2 4 34.8
3 1 30.8
3 2 27
3 3 35.5
3 4 40.2
1 1 28.2
1 2 24.5
1 3 31.1
1 4 30.7
2 1 30.1
2 2 31.6
2 3 33.6
2 4 31.3
3 1 30.9
3 2 28.4
3 3 35.2
3 4 35.3

005_mzhwa5o-uolrfi52.docx

David · Accepted Answer

Assignment
a) Plot showing 2 x variables: 
 
From the graph showing on x axis ingredient A and y axis ingredient B we 
find that there is not at all a linear correlation between the two.  In other 
words, the two seems to be independent with correlation =0
b) Plot of yield against ingredient A:
Plot of yield against ingredient B:
There are no outliers in ingredient A and in ingredient B.  
Also in yield, there are no outliers.

Use the “CropYield” dataset for this problem. The y -variable is Yield = the yield of a crop during a growing season. There are two x -variables. The variable IngredA = the amount of ingredient A put...

Answer To: Use the “CropYield” dataset for this problem. The y -variable is Yield = the yield of a crop during...

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