Predictive Analytics
CME Group Foundation Business Analytics Lab
Jax Farquhar
March 6, 2018
Notebook Instructions
For your assignment you may be using different dataset than what is included here.
Always read carefully the instructions on Sakai.
Tasks/questions to be completed/answered are highlighted in larger bolded fonts and numbered according to their section.
About
In a given year, if it rains more, we may see that there might be an increase in crop production. This is because more water may lead to more plants.
This is a direct relationship; the number of fruits may be able to be predicted by amount of waterfall in a certain year.
This example represents simple linear regression, which is an extremely useful concept that allows us to predict values of a certain variable based off another variable.
This lab will explore the concepts of simple linear regression, multiple linear regression, and watson analytics.
Load Packages in R/RStudio
We are going to use tidyverse a collection of R packages designed for data science.
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## layoutTask 1: Correlation Analysis
1A) Read the csv file into R Studio and display the dataset.
Name your dataset ‘mydata’ so it easy to work with.
Commands: read_csv() rename() head()
Extract the assigned features (columns) to perform some analytics.
mydata = read.csv(file="Advertising.csv")
head(mydata)## X TV radio newspaper sales
## 1 1 230.1 37.8 69.2 22.1
## 2 2 44.5 39.3 45.1 10.4
## 3 3 17.2 45.9 69.3 9.3
## 4 4 151.5 41.3 58.5 18.5
## 5 5 180.8 10.8 58.4 12.9
## 6 6 8.7 48.9 75.0 7.2sales <- mydata$sales
radio <- mydata$radio
newspaper <- mydata$newspaper
TV <- mydata$TV1B) Create a correlation table for your to compare the correlations between all variables. Remove any variables where correlation between variables is irrelevant or inaccurate
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layoutShow in New WindowClear OutputExpand/Collapse Output
X
#corr = cor( MYDATA )
#corr
corr = cor(mydata[ -c(1) ])
corr## TV radio newspaper sales
## TV 1.00000000 0.05480866 0.05664787 0.7822244
## radio 0.05480866 1.00000000 0.35410375 0.5762226
## newspaper 0.05664787 0.35410375 1.00000000 0.2282990
## sales 0.78222442 0.57622257 0.22829903 1.00000001C) Why is the value “1.0” down the diagonal? Which pairs seem to have the strongest correlations, list the pairs.
In each collumn, one variable will have a perfect correlation with itself. The relationship between TV and TV will always be 1. TV and sales, radio and sales have the strongest correlations or the correlations closest to one.
1D-a) Identifying the dependent variable (y) and one independent variable (x_i) using the correlation table to identify a variable with a coefficient greater than 0.20 and lower than 0.60. Use those two variables to create a scatterplot to visualize the data. Note any patterns or relation between the two variables
- Commands: qplot( x = VARIABLE, y = VARIABLE, data = mydata)
qplot( x =radio, y = sales, data = mydata)
The relationship between sales and radio is postively correlated, because the points on the graph move up and to the right. The correlation coefficient of radio and sales is 0.57622257; which can be seen in the correlation chart
Task 2: Regression Analysis
- To create a regression model we use the function lm(), such as lm( y ~ x )
- Where the independent variable or variables [ x_1, x_2, … x_i ], predict the values of the dependent variable y.
2A) Create a linear regression model by identifying the dependent variable (y) and for independent variable (x_i) use the correlation table to identify a variable with a coefficient greater than 0.20 and lower than 0.60. (same variables as 1D-a)
- Commands: lm( y ~ x )
#Simple Linear Regression Model
#reg <- lm( DEPENDENT_VARIABLE ~ INDEPENDENT_VARIABLE )
reg <- lm( sales ~ radio )2B) Use the regression model to create a report. Note the R-Squared and Adjusted R-Squared values, determine if this is a good or bad fit for your data?
- Commands: Use the summary() function to create a report for the linear model
#Summary of Simple Linear Regression Model
#summary(MODEL)
summary(reg)##
## Call:
## lm(formula = sales ~ radio)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.7305 -2.1324 0.7707 2.7775 8.1810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.31164 0.56290 16.542 <2e-16 ***
## radio 0.20250 0.02041 9.921 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.275 on 198 degrees of freedom
## Multiple R-squared: 0.332, Adjusted R-squared: 0.3287
## F-statistic: 98.42 on 1 and 198 DF, p-value: < 2.2e-16The R-Squared is .332 and the Adjusted R-squared is .3287 anything below .5 indicates that it’s a bad fit for the data.
Y_mpg_predicted = intercept estimate value +/- intercept weight estimate * (weight) sales = 9.3116 - (0.20250) * (radio) to change from scientific values options (scipen = 9999) -> changes output to complete numbers rather than e
2C) Create a plot for the dependent (y) and independent (x) variables Note any patterns or relation between the two variables describe the trend line.
- The trend line will show how far the predictions are from the actual value
- The distance from the actual versus the predicted is the residual
#p <- qplot( x = INDEPENDENT_VARIABLE, y = DEPENDENT_VARIABLE, data = mydata) + geom_point()
p <- qplot( x = radio, y = sales, data = mydata) + geom_point()
p
#Add a trend line plot using the a linear model
#p + geom_smooth(method = "lm", formula = y ~ x)
p + geom_smooth(method = "lm", formula = y ~ x)
2D-b) Create a Multiple Linear Regression Model using all relevant independent variables and the dependent variable. Note the R-Squared and Adjusted R-Squared values, determine if this is a good or bad fit for your data?
y = 2.92110 + 0.04575*(mydata$TV) + 0.18799*(mydata$radio)
y## [1] 20.554197 12.344982 12.336741 17.616212 13.222992 12.511836 11.717797
## [8] 12.104854 3.709329 12.550724 7.035517 17.255385 10.608399 8.810449
## [15] 18.443546 20.827773 12.903384 23.239554 9.940795 14.153036 18.120223
## [22] 14.740899 6.514041 16.542856 8.139999 15.606740 14.966882 17.045108
## [29] 19.398229 9.158890 21.641392 11.357301 7.649985 18.832100 7.562561
## [36] 16.991384 23.365737 15.625331 9.912258 20.439323 16.377652 17.297716
## [43] 21.560623 13.965891 8.900768 15.161700 8.885976 21.698110 16.285742
## [50] 8.181258 12.644719 9.319104 20.660583 19.960188 20.353737 21.307481
## [57] 8.537594 12.761658 21.889504 18.106330 5.744705 22.902748 16.782920
## [64] 13.184129 16.964897 7.826157 8.986779 12.019930 18.951875 21.092461
## [71] 17.782419 10.632707 10.350870 9.912693 17.308704 11.909438 4.480009
## [78] 13.791690 8.789051 9.675623 11.435733 14.662709 10.182272 14.415955
## [85] 20.772295 15.219016 11.581550 15.618019 11.754570 16.930372 9.986476
## [92] 4.511535 19.178540 21.261410 10.466510 16.332559 12.619265 15.328065
## [99] 24.126852 16.945683 13.904257 23.305437 17.638949 14.750953 20.266807
## [106] 17.952761 6.132740 7.113297 3.595621 19.662581 14.792968 21.122495
## [113] 13.854421 16.382894 15.296682 12.936575 11.977757 6.566792 15.608706
## [120] 6.816490 14.423707 7.860583 13.620276 15.057379 19.492802 9.128782
## [127] 10.590761 6.590250 22.211335 7.903680 10.397529 15.599171 8.418728
## [134] 19.274615 11.865689 13.966355 11.423910 20.875786 9.757291 19.633036
## [141] 9.474980 18.437721 19.250243 8.778093 10.104502 9.697006 15.278002
## [148] 23.259010 12.235597 9.816267 18.376186 10.035966 16.341467 18.221278
## [155] 15.479539 5.289359 15.394590 10.018837 10.393206 12.405391 14.215594
## [162] 13.571917 14.943019 17.319257 11.046453 14.288641 10.808449 13.359748
## [169] 17.212214 17.920519 7.389284 14.375966 7.596399 11.960129 13.735066
## [176] 24.781986 19.962698 12.174072 16.012502 12.377200 10.574324 13.932621
## [183] 6.563793 24.162370 18.536637 20.778199 9.698004 17.059238 18.618661
## [190] 6.051304 12.454614 8.405517 4.478759 18.447780 16.462319 5.364313
## [197] 8.151901 12.767157 23.791380 15.156389Based purely on the values for R-Squared and Adjusted R-Squared, which linear regression model is best in predicting the dependent variable? Explain why
The multiple linear regression model is better because it is higher meaning there is a better chance of it being correct.
2E) Use the three different models to predicted the dependent variable for the given values of the independent variables.
- Variable: Radio = 69
- Variable: TV = 255
- Variable: newspaper = 75
MODEL 1
reg <- lm(mydata$sales ~ mydata$radio)
reg##
## Call:
## lm(formula = mydata$sales ~ mydata$radio)
##
## Coefficients:
## (Intercept) mydata$radio
## 9.3116 0.2025y = 0.2025*(69) + 9.3116
y## [1] 23.2841MODEL 2
reg <- lm(mydata$sales ~ mydata$newspaper)
reg##
## Call:
## lm(formula = mydata$sales ~ mydata$newspaper)
##
## Coefficients:
## (Intercept) mydata$newspaper
## 12.35141 0.05469y = 0.05469 + 12.35141*75
y## [1] 926.4104MODEL 3
mlrl <- lm(mydata$radio ~ mydata$TV + mydata$newspaper)
mlrl##
## Call:
## lm(formula = mydata$radio ~ mydata$TV + mydata$newspaper)
##
## Coefficients:
## (Intercept) mydata$TV mydata$newspaper
## 15.043008 0.006029 0.240052y = 0.240052*75+0.006029*255+15.043008
y## [1] 34.5843Task 3: Watson Analysis
To complete the last task, follow the directions found below. Make sure to screenshot and attach any pictures of the results obtained or any questions asked.
3A) Use the Predictive module to analyze the given data. Note any interesting patterns add an screenshot of what you found.
knitr::include_graphics('SalesPredictors.png')
TV and radio combined are the strongest correlators of sales
knitr::include_graphics('SalesPredictors2.png')
see above for analysis ### 3B) Note the predictive power strength of reported variables. Consider the one field predictive model only, describe your findings and add and screenshot
knitr::include_graphics('SalesPredictors3.png')
It’s interesting that TV is a better predictor of Sales than Radio. It should also be noted that single correlations are a lot weaker than multiple variable correlations.
3C) How do Watson results reconcile with your findings based on the R regression analysis in task 2? Explain how.
Watson results reconcile with my findings based on the R regression analysis in task 2 because the numbers are fairly similar. Sales and TV have high correlations and next come radio and sales. Generally Radio and TV are important and correlate strongly with Sales.