Quiz4
Cooper Varano
- Q1
empirical ruleYour favorite orange juice brand is Citrus Hill. You went to a local market and found that it is sold at $2.20. You are surprised at the price tag, which seems too pricey. You wonder how rare it would be to encounter a Citrus Hill orange juice at this price. Fortunately, you have a dataset of the Citrus Hill juice prices. How would you use the dataset to answer your question? Describe. - Q2
PriceCHIs the data normally distributed? Plot Citrus Hill orange juice price in a histogram. - Q3
PriceCHCalculate the mean of price. - Q4
PriceCHCalculate the standard deviation of price. - Q5
empirical ruleBase on your analysis in Q2, would it be appropriate to use the empirical rule for Q1? Why? Why not? - Q6
empirical ruleLet’s just assume that the prices are normally distributed for the sake of discussion. Would you pay $2.20 for the Citrus Hill orange juice? Or walk away? - Q7 Why do you think the empirical rule uses the standard deviation as a measure of spread instead of the variance?
- Q8 Hide the messages, but display the code and its results on the webpage.
- Q9 Display the title and your name correctly at the top of the webpage.
- Q10 Use the correct slug.
knitr::opts_chunk$set(echo = FALSE)For this quiz, you are going to use orange juice data. This data set is originally used in a machine learning (ML) class, with the goal to predict which of the two brands of orange juices the customers bought. Of course, you are not building a ML algorithm in this quiz. I just wanted to provide you with the context of the data.
The response variable (that ML algorithm is built to predict) is Purchase, which takes either CH (Citrus Hill) or MM (Minute Maid). The predictor variables (that ML algorithm uses to make predictions) are characteristics of the customer and the product itself. Together, the data set has 18 variables.WeekofPurchase is the week of purchase. LoyalCH is customer brand loyalty for CH (how loyal the customer is for CH on a scale of 0-1), and is the only variable that characterizes customers. All other variables are characteristics of the product or stores the sale occurred at. For more information on the data set, click the link below and scroll down to page 11. https://cran.r-project.org/web/packages/ISLR/ISLR.pdf
## -- Attaching packages -------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.3 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0## -- Conflicts ----------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()## Purchase WeekofPurchase StoreID PriceCH PriceMM DiscCH DiscMM SpecialCH
## 1 CH 237 1 1.75 1.99 0.00 0.0 0
## 2 CH 239 1 1.75 1.99 0.00 0.3 0
## 3 CH 245 1 1.86 2.09 0.17 0.0 0
## 4 MM 227 1 1.69 1.69 0.00 0.0 0
## 5 CH 228 7 1.69 1.69 0.00 0.0 0
## 6 CH 230 7 1.69 1.99 0.00 0.0 0
## SpecialMM LoyalCH SalePriceMM SalePriceCH PriceDiff Store7 PctDiscMM
## 1 0 0.500000 1.99 1.75 0.24 No 0.000000
## 2 1 0.600000 1.69 1.75 -0.06 No 0.150754
## 3 0 0.680000 2.09 1.69 0.40 No 0.000000
## 4 0 0.400000 1.69 1.69 0.00 No 0.000000
## 5 0 0.956535 1.69 1.69 0.00 Yes 0.000000
## 6 1 0.965228 1.99 1.69 0.30 Yes 0.000000
## PctDiscCH ListPriceDiff STORE
## 1 0.000000 0.24 1
## 2 0.000000 0.24 1
## 3 0.091398 0.23 1
## 4 0.000000 0.00 1
## 5 0.000000 0.00 0
## 6 0.000000 0.30 0## Rows: 1,070
## Columns: 18
## $ Purchase <fct> CH, CH, CH, MM, CH, CH, CH, CH, CH, CH, CH, CH, CH, ...
## $ WeekofPurchase <int> 237, 239, 245, 227, 228, 230, 232, 234, 235, 238, 24...
## $ StoreID <fct> 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 2...
## $ PriceCH <dbl> 1.75, 1.75, 1.86, 1.69, 1.69, 1.69, 1.69, 1.75, 1.75...
## $ PriceMM <dbl> 1.99, 1.99, 2.09, 1.69, 1.69, 1.99, 1.99, 1.99, 1.99...
## $ DiscCH <dbl> 0.00, 0.00, 0.17, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00...
## $ DiscMM <dbl> 0.00, 0.30, 0.00, 0.00, 0.00, 0.00, 0.40, 0.40, 0.40...
## $ SpecialCH <int> 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ SpecialMM <int> 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1...
## $ LoyalCH <dbl> 0.500000, 0.600000, 0.680000, 0.400000, 0.956535, 0....
## $ SalePriceMM <dbl> 1.99, 1.69, 2.09, 1.69, 1.69, 1.99, 1.59, 1.59, 1.59...
## $ SalePriceCH <dbl> 1.75, 1.75, 1.69, 1.69, 1.69, 1.69, 1.69, 1.75, 1.75...
## $ PriceDiff <dbl> 0.24, -0.06, 0.40, 0.00, 0.00, 0.30, -0.10, -0.16, -...
## $ Store7 <fct> No, No, No, No, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Y...
## $ PctDiscMM <dbl> 0.000000, 0.150754, 0.000000, 0.000000, 0.000000, 0....
## $ PctDiscCH <dbl> 0.000000, 0.000000, 0.091398, 0.000000, 0.000000, 0....
## $ ListPriceDiff <dbl> 0.24, 0.24, 0.23, 0.00, 0.00, 0.30, 0.30, 0.24, 0.24...
## $ STORE <fct> 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2...## Purchase WeekofPurchase StoreID PriceCH PriceMM
## CH:653 Min. :227.0 1 :157 Min. :1.690 Min. :1.690
## MM:417 1st Qu.:240.0 2 :222 1st Qu.:1.790 1st Qu.:1.990
## Median :257.0 3 :196 Median :1.860 Median :2.090
## Mean :254.4 4 :139 Mean :1.867 Mean :2.085
## 3rd Qu.:268.0 7 :355 3rd Qu.:1.990 3rd Qu.:2.180
## Max. :278.0 NA's: 1 Max. :2.090 Max. :2.290
## NA's :1 NA's :4
## DiscCH DiscMM SpecialCH SpecialMM
## Min. :0.00000 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
## Median :0.00000 Median :0.0000 Median :0.000 Median :0.0000
## Mean :0.05196 Mean :0.1234 Mean :0.147 Mean :0.1624
## 3rd Qu.:0.00000 3rd Qu.:0.2300 3rd Qu.:0.000 3rd Qu.:0.0000
## Max. :0.50000 Max. :0.8000 Max. :1.000 Max. :1.0000
## NA's :2 NA's :4 NA's :2 NA's :5
## LoyalCH SalePriceMM SalePriceCH PriceDiff Store7
## Min. :0.000011 Min. :1.190 Min. :1.390 Min. :-0.6700 No :714
## 1st Qu.:0.320000 1st Qu.:1.690 1st Qu.:1.750 1st Qu.: 0.0000 Yes:356
## Median :0.600000 Median :2.090 Median :1.860 Median : 0.2300
## Mean :0.565203 Mean :1.962 Mean :1.816 Mean : 0.1463
## 3rd Qu.:0.850578 3rd Qu.:2.130 3rd Qu.:1.890 3rd Qu.: 0.3200
## Max. :0.999947 Max. :2.290 Max. :2.090 Max. : 0.6400
## NA's :5 NA's :5 NA's :1 NA's :1
## PctDiscMM PctDiscCH ListPriceDiff STORE
## Min. :0.00000 Min. :0.00000 Min. :0.000 0 :356
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.140 1 :157
## Median :0.00000 Median :0.00000 Median :0.240 2 :222
## Mean :0.05939 Mean :0.02732 Mean :0.218 3 :194
## 3rd Qu.:0.11268 3rd Qu.:0.00000 3rd Qu.:0.300 4 :139
## Max. :0.40201 Max. :0.25269 Max. :0.440 NA's: 2
## NA's :5 NA's :2Q1 empirical rule Your favorite orange juice brand is Citrus Hill. You went to a local market and found that it is sold at $2.20. You are surprised at the price tag, which seems too pricey. You wonder how rare it would be to encounter a Citrus Hill orange juice at this price. Fortunately, you have a dataset of the Citrus Hill juice prices. How would you use the dataset to answer your question? Describe.
I would first find the mean of the data, after distribution you can find the deviations from the mean Hint: Discuss all of the following topics in your answer: the normal distribution, the mean, and the standard deviation.
Q2 PriceCH Is the data normally distributed? Plot Citrus Hill orange juice price in a histogram.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 1 rows containing non-finite values (stat_bin).
Q3 PriceCH Calculate the mean of price.
## [1] 1.867428``Hint: You may add thena.rm = TRUE` argument in the mean() function, if the function returns NA. It means that the variable has at least one row with NA.
Q4 PriceCH Calculate the standard deviation of price.
Hint: You may add the na.rm = TRUE argument in the mean() function, if the function returns NA. It means that the variable has at least one row with NA.
## [1] 0.1020172The standard deviation is 0.1
Q5 empirical rule Base on your analysis in Q2, would it be appropriate to use the empirical rule for Q1? Why? Why not?
Hint: Discuss characterstics of the normal distribution.
Yes i would use the empirical rule for question 1, most of the sales are within the range of SD. By using this rule you can find your probability.
Q6 empirical rule Let’s just assume that the prices are normally distributed for the sake of discussion. Would you pay $2.20 for the Citrus Hill orange juice? Or walk away?
I would walk away because the mean is $1.80 and the price is $2.20
Hint: Discuss in terms of the mean, the standard deviation, and the probability.
Q7 Why do you think the empirical rule uses the standard deviation as a measure of spread instead of the variance?
Hint: Discuss in terms of the unit of the variance and the standard deviation.
The empirical rule uses the standard deviation as a measure of spread instead of the variance. Variance isnt measured the same as distribution.
Q8 Hide the messages, but display the code and its results on the webpage.
Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.