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Linear regression
Related Topics
Wize University Statistics Textbook > Inference for Linear Regression
Simple Linear Regression Analysis
3 Activities
Using the information provided below, solve for the slope and intercept of the linear regression equation.
∑
x
=
702
∑
y
=
461
∑
x
y
=
19
,
871
∑
x
2
=
31396
∑
y
2
=
13
,
449
\begin{array}{ll}\sum x=702\\\sum y=461\\\sum xy=19,871\\\sum x^2=31396\\\sum y^2=13,449\end{array}
∑
x
=
702
∑
y
=
461
∑
x
y
=
19
,
871
∑
x
2
=
31396
∑
y
2
=
13
,
449
n
=
18
n=18
n
=
18
Click on 'HINT' if you are stuck!
(i) What is the slope? [Provide answer with at least 2 decimal places.]
(ii) What is the intercept? [Provide answer with at least 2 decimal places.]
I don't know
Check Submission
More Simple Linear Regression Analysis Questions:
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Linear Regression Analysis
The regression model
y
=
4000
−
2.7
x
y=4000-2.7x
y
=
4000
−
2.7
x
is used to estimate the annual number of
cars going over the speed limit (y) based on the number of police officers on
the road. Estimate the number of cars going over the speed limit when there are
Linear Regression: Residual Plots
The equation
y
^
=
35
+
1.50
x
\hat{y}=35+1.50x
y
^
=
35
+
1.50
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience.
Elizabeth has 4 years of experience and earns $36 per hour. What is the residual?
Linear regression
Savage question!
(iv) What body fat % would you predict for Mike who is turning 32 years old?
∑
x
=
702
∑
y
=
461
∑
x
y
=
19
,
871
∑
x
2
=
31396
∑
y
2
=
13
,
449
\begin{array}{ll}\sum x=702\\\sum y=461\\\sum xy=19,871\\\sum x^2=31396\\\sum y^2=13,449\end{array}
∑
x
=
702
∑
y
=
461
∑
x
y
=
19
,
871
∑
x
2
=
31396
∑
y
2
=
13
,
449
Linear Regression Analysis
Suppose we want to see if there is a relationship between the size of a condo unit in Twin Pines and its selling price. We randomly sampled 32 units:
What is the explanatory variable (X)?
Simple Linear Regression Analysis
Given the information below, find the slope and intercept of the regression line. [Provide at least one decimal place, e.g. 8.2. Include negative sign if negative, e.g. -3.9.]
Linear Regression
Parts (a) to (c) are based on the following information.
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience. The correlation is
r
=
0.56
r=0.56
r
=
0.56
. Suppose that
x
x
x
is changed to
months
of experience.
(a) Which of the following will be the correct regression line?
Correlation and Residual Plots
Pamela and Tim are trying to be healthy by taking the stairs instead of the elevator. We want to see there is a relationship between the floor you live on and the time it takes to get to your floor from the lobby. Pamela lives on the 8th floor. Tim lives in the penthouse on the 20th floor.
∑
x
2
=
258
\sum_{ }^{ }x^2=258
∑
x
2
=
258
∑
y
2
=
687
\sum_{ }^{ }y^2=687
∑
y
2
=
687
Simple Linear Regression: Correlation
True or false? Enter T if True, F if False. (Use capital letters: T, F)
1. If 𝒓 = −𝟏. 𝟎𝟎, then 100% of the data points fall exactly on the regression line and the slope cannot be equal or greater than 0.
T
Predictions and Residual Plots
The equation
y
^
\hat{y}
y
^
=35+1.50
x
x
x
is used to predict the hourly wage
y
y
y
of someone with
x
x
x
years
of experience.
(c) Elizabeth has 4 years of experience and earns $36. What is the residual?
Simple Linear Regression
Here is a residual plot for selling price (Y) vs. size of a condo in square-feet (X).
Which condition is violated?