Question

Select at least three variables that you believe have a linear relationship.

A. Specify which variable is dependent and which are independent.

B. Collect the data for these variables and describe your data collection technique and why it was appropriate as well as why the sample size was best.

C. Submit the data collected by submitting the SPSS data file with your submission.

D. Find the Correlation coefficient for each of the possible pairings of dependent and independent variables and describe the relationship in terms of strength and direction.

E. Find a linear model of the relationship between the three (or more) variables of interest.

F. Explain the validity of the model.

Answer #1

temperature is dependent variable, latitude, longitude and elevation are independent

Source Sum square DF Mean square

Total 181439 1069 170

Error 25301 1066 24

Regression 156138 3 52046

F = 52046/24 ≈ 2169 on 3,1066 DF

The relative importance of the variables can be assessed based on the PVE’s for various submodels:

Predictors PVE F

Latitude 0.75 1601

Longitude 0.10 59

Elevation 0.02 9

Longitude, Elevation 0.19 82

Latitude, Elevation 0.75 1080

Latitude, Longitude 0.85 2000

Latitude, Longitude, Elevation 0.86 1645

Latitude is by far the most important predictor, with longitude a distant second.

Up to this point, each predictor variable has been incorporated into the regression function through an additive term βiXi . Such a term is called a main effect.

r the temperature data, each of the three possible interactions was added (individually) to the model along with the three main effects. PVE’s and F statistics are given below:

Interactions PVE F

Latitude×Longitude 0.88 1514

Latitude×Elevation 0.86 1347

Longitude×Elevation 0.88 1519

The coefficients for the model including the latitude×longitude interaction are:

E(Y |X) = 188 − 4.25Latitude + 0.61Longitude − 0.003Elevation + 0.02Latitude × Longitude

Longitude ranges from 68◦ to 125◦ in this data set.

Thus in the western US the model can be approximated as E(Y |X) ≈ 264 − 1.75Latitude − 0.003Elevation,

while in the eastern US, the model can be aproximated as E(Y |X) ≈ 229 − 2.89Latitude − 0.003Elevation.

This tells us that the effect of latitude was stronger in the eastern US than in the western US.

Data needs to be analyzed
For this assignment I have to analyze the regression
(relationship between 2 independent variables and 1 dependent
variable). Below is all of my data and values. I need help
answering the questions that are at the bottom. Questions regarding
the strength of the relationship
Sum of X1 = 184.6
Sum of X2 = 21307.03
Sum of Y = 2569.1
Mean X1 = 3.6196
Mean X2 = 417.7849
Mean Y = 50.3745
Sum of squares (SSX1)...

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(Method 1), Hybrid (Method 2), and online (Method 3). You randomly
sample students from two different schools (A and B) and from three
different classrooms per school that exclusively uses one of the
methods. The data that you collect (eight students per classroom)
are final semester achievement scores as follows:
Method
1
Method 2
Method 3
School
A
55,55,55,60
60,60,65,65
65,70,70,70,...

Data Set Preparation
(Using A JMP Folder) Can email you if comment your email.
1. (10 pts.) Using the “Toyota Corolla” data set on Canvas (Home
à “JMP” à “(Under: JMP Data Sets folder)”, you will be modeling the
“Price” of a car as the dependent variable (Y). Please select one
independent variable (X) you think may help explain Price, from the
following three: “Age”, “Mileage”, or “Weight” of a car. In the
space below, state your choice and explain...

Part C: Regression and Correlation Analysis
Use the dependent variable (labeled Y) and the independent
variables (labeled X1, X2, and X3) in the data file. Use Excel to
perform the regression and correlation analysis to answer the
following.
Generate a scatterplot for the specified dependent variable (Y)
and the X1 independent variable, including the graph of the "best
fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
the relationship between the dependent variable and the selected...

Use the dependent variable (labeled Y) and the independent
variables (labeled X1, X2, and X3) in the data file. Use Excel to
perform the regression and correlation analysis to answer the
following.
Generate a scatterplot for the specified dependent variable (Y)
and the X1 independent variable, including the graph of the "best
fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
the relationship between the dependent variable and the selected
independent variable.
Determine the coefficient of...

Multiple Choice
Select the best answer from the available choices for each
question.
Which of the following is NOT part of the definition of
a sample space S?
S can be discrete or continuous
Each outcome must be in S at most once
Each element in S is equally likely
Each outcome must be in S at least once
S is a set of possible outcomes in an experiment
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Bivariate Data & Probability
After completing the calculation by hand in Q1 you can use
Excel to check your answers before submitting. Q2 assesses your
general understanding of probability and linear associations using
Excel to analyse a large dataset.
Question 1
Covariance and Correlation
The table below shows a set of sample bivariate data. Calculate
the covariance and correlation coefficient by completing the below
table. Show all working.
X
Y
(X - )
(Y - )
(X - )(Y -...

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