In: Math

name and draw two diagnostic plots used to evaluate linear regression and how they would look if all model assumptions are met.

**1. Residuals vs Fitted**

This plot shows if residuals have non-linear patterns. There could be a non-linear relationship between predictor variables and an outcome variable and the pattern could show up in this plot if the model doesn’t capture the non-linear relationship. If you find equally spread residuals around a horizontal line without distinct patterns, that is a good indication you don’t have non-linear relationships.

Let’s look at residual plots from a ‘good’ model and a ‘bad’ model. The good model data are simulated in a way that meets the regression assumptions very well, while the bad model data are not.

What do you think? Do you see differences between the two cases? I don’t see any distinctive pattern in Case 1, but I see a parabola in Case 2, where the non-linear relationship was not explained by the model and was left out in the residuals.

**2. Normal Q-Q**

This plot shows if residuals are normally distributed. Do residuals follow a straight line well or do they deviate severely? It’s good if residuals are lined well on the straight dashed line.

What do you think? Of course they wouldn’t be a perfect straight line and this will be your call. Case 2 definitely concerns me. I would not be concerned by Case 1 too much, although an observation numbered as 38 looks a little off. Let’s look at the next plot while keeping in mind that #38 might be a potential problem

How to detect heteroscedasticity in the regression model? Look
at the residual plots against each independent predictor. A “V” or
“U” shape pattern indicates that the error terms do not have
homogeneous variance. true or false

Describe how simple linear regression analysis and
multiple regression are used to support areas of industry research,
academic research, and scientific research.

explain how linear regression could be used in business decision
making?

Linear Regression
Linear regression is used to predict the value of one variable
from another variable. Since it is based on correlation, it cannot
provide causation. In addition, the strength of the relationship
between the two variables affects the ability to predict one
variable from the other variable; that is, the stronger the
relationship between the two variables, the better the ability to
do prediction.
What is one instance where you think linear regression
would be useful to you in...

Discuss the reasons and situations in which researchers would
want to use linear regression. How would a researcher know whether
linear regression would be the appropriate statistical technique to
use? What are some of the benefits of fitting the relationship
between two variables to an equation for a straight line?
Describe the error in the conclusion. Given: There is a linear
correlation between the number of cigarettes smoked and the pulse
rate. As the number of cigarettes increases the pulse...

Discuss the reasons and situations in which researchers would
want to use linear regression. How would a researcher know whether
linear regression would be the appropriate statistical technique to
use? What are some of the benefits of fitting the relationship
between two variables to an equation for a straight line? Describe
the error in the conclusion. Given: There is a linear correlation
between the number of cigarettes smoked and the pulse rate. As the
number of cigarettes increases the pulse...

So, as we look at Linear Regression and correlation this week,
please find provide an example of how and when linear regression is
used.

What statistical information should one look for in order to
determine that a given linear regression model is not a good fit?
If you shouldn't use such a linear model then what would be a good
estimate for a predicted output?

True or False:
-Linear regression is one of the least commonly used regression
techniques.
-The difference between simple linear regression and multiple
linear regression is that, multiple linear regression has (>1)
independent variables, whereas simple linear regression has only 1
independent variable.
-Least Square Method calculates the best-fit line for the
observed data by minimizing the sum of the squares of the
horizontal deviations from each data point to the line.
-We can evaluate the model performance using the metric...

. Draw a plot of the following set of data
and determine the linear regression equation. What is
the
value of the slope and
intercept? What is r and
R2? Are there any outlier
values? (15 points)
Age
(X): 20 25 36 29 41 35 56 43 66 50 59 67 51 75 75 81 54 66 52 48
Total Body
Water
(Y): 61 57 52 59 53 58 48 51 37 44 42 41 48 38 41 39 47 42 51 50

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