Project 2
Emma LaBombard
2024-04-02
#Training & Testing the Model
knitr::opts_chunk$set(echo = FALSE)
t_train <- prepared_data %>%
filter(year_sold == 2006 | year_sold == 2007 | year_sold == 2008 | year_sold == 2009)
t_test <- prepared_data %>%
filter(year_sold == 2010)Histograms
Correlation
Model
##
## Call:
## lm(formula = sale_price ~ year_built + garage_area + mas_vnr_area +
## overall_qual_as_num + total_bsmt_sf, data = t_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -201501 -21204 -3191 15837 232248
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -238228.608 78869.887 -3.021 0.00257 **
## year_built 85.831 41.726 2.057 0.03987 *
## garage_area 65.272 5.475 11.922 < 0.0000000000000002 ***
## mas_vnr_area 67.082 6.896 9.728 < 0.0000000000000002 ***
## overall_qual_as_num 28350.228 1011.535 28.027 < 0.0000000000000002 ***
## total_bsmt_sf 38.288 2.848 13.444 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35940 on 1399 degrees of freedom
## Multiple R-squared: 0.7677, Adjusted R-squared: 0.7669
## F-statistic: 924.6 on 5 and 1399 DF, p-value: < 0.00000000000000022RSME & R^2
#RSME
t_train <- t_train %>%
mutate(predicted = predict(model, newdata = t_train),
residual = predicted - sale_price)
mean(t_train$residual)## [1] -0.0000000003143103rsme_train = sqrt(mean(t_train$residual^2))
print(rsme_train)## [1] 35863.4t_test <- t_test %>%
mutate(predicted = predict(model, newdata = t_test),
residual = predicted - sale_price)
mean(t_test$residual)## [1] -2467.148rsme_test = sqrt(mean(t_test$residual^2))
print(rsme_test)## [1] 36804.88#R^2
#train
residual_sum_of_squares <- sum(t_train$residual^2)
total_variation_in_model <-mean(t_train$sale_price) - t_train$sale_price
total_sum_of_squares <- sum(total_variation_in_model^2)
r2 <- 1-(residual_sum_of_squares/total_sum_of_squares)
print(c('r-squared for train', r2))## [1] "r-squared for train" "0.767681562286635"#test
sum_squared_error <- sum(t_test$residual^2)
diff_of_mean <- mean(t_test$residual) - t_test$residual
squared_var <- sum(diff_of_mean^2)
r2 <- 1-(squared_var/diff_of_mean)
print(c('r-squared for test', r2))## 1 2
## "r-squared for test" "4838602.24054263" "99521422.6277849"
## 3 4 5
## "-5392492.70429925" "20158230.3368639" "5478778.67718587"
## 6 7 8
## "-4583849.23599076" "5797253.36522829" "-34059930.5905934"
## 9 10 11
## "-296927571.520737" "-35988033.539681" "6559565.24908022"
## 12 13 14
## "5621978.52770792" "3815804.98899747" "-3860663.9401994"
## 15 16 17
## "-4109081.06640097" "10369239.1968261" "3486233.96503932"
## 18 19 20
## "9906944.46074837" "-1085419.78573003" "74408637.1049727"
## 21 22 23
## "-3850748.30720525" "62970105.0853265" "9292506.0500242"
## 24 25 26
## "5095033.40161641" "-27290819.6732714" "23827069.3306999"
## 27 28 29
## "-50745950.9454602" "-17768858.8246254" "-9106825.51515567"
## 30 31 32
## "-70871332.9192792" "-33481621.3561454" "11477371.2125671"
## 33 34 35
## "-22205977.6556592" "-6457586.52066818" "-11488645.2248824"
## 36 37 38
## "9705088.20096276" "-52842205.4766288" "34012693.3622881"
## 39 40 41
## "3924975.40718116" "38572795.6546105" "-31910137.8955216"
## 42 43 44
## "35337757.2622817" "175360199.345136" "58705622.6016026"
## 45 46 47
## "26691195.6537062" "-6951925.06543174" "16106814.3558422"
## 48 49 50
## "5836768.66423366" "6458839.72780954" "6213561.02017195"
## 51 52 53
## "8186523.29024328" "6543628.84931619" "6110175.67014597"
## 54 55 56
## "444451279.489116" "25734140.841295" "10589752.314312"
## 57 58 59
## "-48323898.4642103" "44963820.724761" "-10030078.7397473"
## 60 61 62
## "3757786.21621532" "-20755512.2797605" "-6717846.00871418"
## 63 64 65
## "-25560457.1653602" "-7476939.53772072" "20814749.7820656"
## 66 67 68
## "12524539.1411833" "13808105.5383167" "2950794.01969596"
## 69 70 71
## "6448813.01941082" "4748223.2003134" "20346838.4445698"
## 72 73 74
## "-28328634.3799723" "-159558117.687287" "10077816.6485513"
## 75 76 77
## "34601117.0204813" "6418181.03801006" "-32163746.7877587"
## 78 79 80
## "29170916.056941" "24282037.2194222" "11606804.6808812"
## 81 82 83
## "-30209547.3287637" "26264740.4754823" "300493337.434655"
## 84 85 86
## "-25645218.4563155" "-9311540.42968342" "-20031538.8461696"
## 87 88 89
## "-23088494.8671351" "22932696.6129872" "87686977.9050808"
## 90 91 92
## "-85307806.1580801" "13281825.0807522" "13266243.276429"
## 93 94 95
## "-6661283.04229675" "12876394.8759981" "28523904.5876937"
## 96 97 98
## "-297797323.249289" "8197229.56793993" "4901265.09026103"
## 99 100 101
## "-16120108.0645849" "9591198.23313874" "38452030.6862684"
## 102 103 104
## "-13014238.4412343" "29099582.5638882" "26664219.5836726"
## 105 106 107
## "2322914937.71902" "5992498.5760847" "8348059.01963568"
## 108 109 110
## "-18474343.6856413" "-4639122.48278737" "-16856811.4601885"
## 111 112 113
## "212078144.892089" "14642458.8378286" "14290661.3396503"
## 114 115 116
## "88042505.1651527" "15507695.2408896" "4693009.25473404"
## 117 118 119
## "36798246.4808894" "-11750984.116575" "1112820868.31108"
## 120 121 122
## "-22336796.6879761" "53452456.3184043" "-8406039.77056131"
## 123 124 125
## "-2247590.12030139" "-6422368.74240895" "-6424717.51587087"
## 126 127 128
## "-6162930.83876711" "8402023.63131992" "8899091.25651308"
## 129 130 131
## "16964815.2758158" "-3437816.60457575" "5939818.52491619"
## 132 133 134
## "-6901980.53535312" "-30384077.7037884" "14287988.9513976"
## 135 136 137
## "7799458.07837513" "6058829.85669857" "-2933015.93901359"
## 138 139 140
## "-23323081.4960262" "24070333.5943063" "-16433343.2358465"
## 141 142 143
## "142256691.969223" "18342116.2747034" "-21547838.4995492"
## 144 145 146
## "-9605264.33388689" "5971367.92961652" "9832486.07754062"
## 147 148 149
## "5822254.42821318" "-4630358.81120448" "-5246678.47418745"
## 150 151 152
## "-9680630.86940142" "-179060445.780501" "25819689.631743"
## 153 154 155
## "6120110.60813678" "203635633.388585" "69800994.2324864"
## 156 157 158
## "41186048.497241" "-10035987.063012" "-5887100.47239393"
## 159 160 161
## "-3201729.8217045" "-2601728.03086242" "-12731922.7710864"
## 162 163 164
## "-3551570.81406548" "-3893826.97690802" "3451329.29820247"
## 165 166 167
## "7983934.42725758" "-11757335.6628062" "18458135.7650625"
## 168 169 170
## "6861864.91445222" "-4460573.14483371" "-19093153.6998392"
## 171 172 173
## "-3996280.79109905" "-12919496.3662908" "-10740418982.3292"
## 174 175 176
## "33610964.472571" "28770772.6551662" "7426988.15739295"
## 177 178 179
## "201266736.566178" "-49283444.2848259" "-26060151.4527308"
## 180 181 182
## "59419488.6222965" "103654113.541407" "-7016634.97624741"Performance Description
Thesis: The sales price of the houses in Ames, Iowa area are influenced by the overall quality of the house, including garage area and basement square foot.
Variables:
Overall Quality: Looks at the quality of different aspects of the house. The data follows a normal distribution with gaps since the quality ratings fell in the areas of poor, fair, average, good, and excellent. This variable had the strongest positive correlation out of all my variables with the sales price. The quality is similar to the value of the house which is what people look for when purchasing a new home and why this variable plays a large role in determining sales price.
Year Built: States when the building was constructed. This variable was one of my less correlated variables to sales price, but still had a positive correlation. The data of houses is left-skewed slightly, showing more houses have been built in the 2000’s than the 1900’s which may hint to a higher price for houses since more are being built.
Garage Area: Here,the amount of space in the garage is given in squared feet. The data is fairly uniform and is slightly right-skewed, meaning most garages are around 500-600 square feet. There seem to be more houses with larger garage square footage, but they are spread out and differ in the actual square footage. The positive correlation between garage area and the sales price shows that the price goes up with a garage included in the house. If people want garages, that will make the price increase.
Total Basement Square Foot: The amount of basement space is given in squared feet. This variable had the lowest standard error or the least amount of discrepancy in the data. With this being the most accurate variable, it provides a reliable measure to help determine the sales price.
Masonry Veneer Area: If the house has any type of brick, this metric displays the measure of how much is on the outside of the house. While the data is right-skewed, there is a positive relationship with sales price. When veneer is present the house costs more and when there is more of the veneer on the house the price continues to rise. While not as significant as the other variables, it still adds to predicting the sales price of the houses.
Predicted Values and Errors: The residual standard error is extremely large. This means that the predicted variables vary drastically from what the true sales price is. Since the predicted variables at large are not accurate, that means they are not the most reliable to predict the sales price.
Visuals/Graphs
ggplot() +
geom_abline(intercept = 0, slope = 1, color = 'purple') +
geom_point(data = t_test,
mapping = aes(x = predicted, y = sale_price),
color = 'blue') +
geom_point(data = t_train,
mapping = aes(x = predicted, y = sale_price),
color = 'orange') 