Stats_Week_8
Vivek Chandra
2023-10-22
# Importing the packages and reading the data set
library(readr)
library(stats)
library(ggplot2)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.2 ✔ stringr 1.5.0
## ✔ forcats 1.0.0 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library(pwr)
library(effsize)
my_data <- read_delim("C:/Users/user/Documents/Statistics/Telangana_2018_complete_weather_data.csv",delim=",")## Rows: 230384 Columns: 10
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): District, Mandal, Location, Date
## dbl (6): row_id, temp_min, temp_max, humidity_min, humidity_max, wind_speed
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Select a continuous (or ordered integer) column of data that seems most “valuable” given the context of your data, and call this your response variable.
Select a categorical column of data (explanatory variable) that you expect might influence the response variable
Devise a null hypothesis for an ANOVA test given this situation. Test this hypothesis using ANOVA, and summarize your results.
Response Variable(continuous column) : humidity_max.
Explanatory variable(categorical column) : District.
Null Hypothesis (H0): The means of “humidity_max” are equal for all districts.
Alternative Hypothesis (H1): The means of “humidity_max” are not equal for at least one district.
anova_result <- aov(humidity_max ~ District, data = my_data)
summary(anova_result)## Df Sum Sq Mean Sq F value Pr(>F)
## District 30 4112839 137095 640.1 <2e-16 ***
## Residuals 230353 49339602 214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tukey_result <- TukeyHSD(anova_result)
p_values <- tukey_result$District[,4]
alpha<- 0.05
significant_comparisons <- sum(p_values < alpha)
if (significant_comparisons > 0) {
cat("Reject the null hypothesis. At least one district has a significantly different mean 'humidity_max'.\n")
} else {
cat("Fail to reject the null hypothesis. There is no significant difference in mean 'humidity_max' among districts.\n")
}## Reject the null hypothesis. At least one district has a significantly different mean 'humidity_max'.Find at least one other continuous (or ordered integer) column of data that might influence the response variable. Make sure the relationship between this variable and the response is roughly linear.
Build a linear regression model of the response using just this column, and evaluate its fit.
Run appropriate hypothesis tests and summarize their results. Use diagnostic plots to identify any issues with your model.
Interpret the coefficients of your model, and explain how they relate to the context of your data
Another Response variable(Continuous Column) : humidity_min
Null Hypothesis (H0): The regression coefficient is equal to zero, indicating that there is no linear relationship between “humidity_min” and “humidity_max.”
Alternative Hypothesis (H1): The regression coefficient of is not equal to zero, suggesting that there is a linear relationship between “humidity_min” and “humidity_max.”
model <- lm(humidity_min ~ humidity_max, data = my_data)
summary(model)##
## Call:
## lm(formula = humidity_min ~ humidity_max, data = my_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -53.866 -11.392 -0.729 11.140 115.780
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -28.840649 0.184191 -156.6 <2e-16 ***
## humidity_max 0.865069 0.002233 387.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.32 on 230382 degrees of freedom
## Multiple R-squared: 0.3945, Adjusted R-squared: 0.3945
## F-statistic: 1.501e+05 on 1 and 230382 DF, p-value: < 2.2e-16p_value <- summary(model)$coefficients["humidity_max", "Pr(>|t|)"]
alpha <- 0.05
if (p_value < alpha) {
cat("Reject the null hypothesis. There is a significant linear relationship between humidity_min and humidity_max.\n")
} else {
cat("Fail to reject the null hypothesis. There is no significant linear relationship between humidity_min and humidity_max.\n")
}## Reject the null hypothesis. There is a significant linear relationship between humidity_min and humidity_max.From the above Hypothesis test, P_value is less than the significance value(alpha) concluding that there is a relationship between humidity_max and humidity_min
Diagnostic plots
# QQ-plot
qqnorm(residuals(model))
qqline(residuals(model))
# Residual plot
plot(model, which = 1)
Include at least one other variable into your regression model (e.g., you might use the one from the ANOVA), and evaluate how it helps (or doesn’t).
Maybe include an interaction term, but explain why you included it.
One other variable (used in First ANOVA) : District
If you want to consider interaction term between “humidity_max” and “District,” . This allow me to assess whether the relationship between “humidity_min” and “humidity_max” varies by district.
interaction_model <- lm(humidity_min ~ humidity_max * District, data = my_data)
summary(interaction_model)##
## Call:
## lm(formula = humidity_min ~ humidity_max * District, data = my_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.922 -11.172 -0.562 10.897 137.032
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -28.844621 0.868712 -33.204
## humidity_max 0.938602 0.011473 81.810
## DistrictBhadradri-Kothagudem -5.618858 2.082859 -2.698
## DistrictHyderabad 5.245200 1.488243 3.524
## DistrictJagtial -16.681932 1.268538 -13.151
## DistrictJangaon 11.860816 1.738170 6.824
## DistrictJayashankar-Bhupalpally -13.821078 1.544230 -8.950
## DistrictJogulamba-Gadwal 6.712413 1.491295 4.501
## DistrictKamareddy -8.304384 1.249201 -6.648
## DistrictKarimnagar -12.233676 1.479667 -8.268
## DistrictKhammam 26.778334 1.628915 16.439
## DistrictKumuram Bheem - Asifabad -10.820434 1.457355 -7.425
## DistrictMahabubabad 4.062261 1.840136 2.208
## DistrictMahabubnagar -5.328168 1.168851 -4.558
## DistrictMancherial -22.462853 1.472347 -15.256
## DistrictMedak -10.045564 1.201180 -8.363
## DistrictMedchal-Malkajgiri 10.891883 1.434804 7.591
## DistrictNagarkurnool -3.667367 1.309563 -2.800
## DistrictNalgonda 22.563203 1.209731 18.651
## DistrictNirmal -10.744748 1.254666 -8.564
## DistrictNizamabad -3.377754 1.135197 -2.975
## DistrictPeddapalli -14.312275 1.669918 -8.571
## DistrictRajanna-Siricilla -4.764673 1.374759 -3.466
## DistrictRangareddy -0.860372 1.142903 -0.753
## DistrictSangareddy -2.884698 1.167676 -2.470
## DistrictSiddipet -2.440627 1.252282 -1.949
## DistrictSuryapet 24.068200 1.588841 15.148
## DistrictVikarabad -4.887130 1.203608 -4.060
## DistrictWanaparthy -2.942661 1.476243 -1.993
## DistrictWarangal (R) -6.833910 1.913256 -3.572
## DistrictWarangal (U) -7.369207 2.027299 -3.635
## DistrictYadadri-Bhongir 18.867377 1.507579 12.515
## humidity_max:DistrictBhadradri-Kothagudem -0.038724 0.023917 -1.619
## humidity_max:DistrictHyderabad -0.102320 0.019496 -5.248
## humidity_max:DistrictJagtial 0.141910 0.015973 8.885
## humidity_max:DistrictJangaon -0.235722 0.021393 -11.019
## humidity_max:DistrictJayashankar-Bhupalpally 0.087651 0.018743 4.676
## humidity_max:DistrictJogulamba-Gadwal -0.140676 0.019678 -7.149
## humidity_max:DistrictKamareddy 0.059778 0.016070 3.720
## humidity_max:DistrictKarimnagar 0.064720 0.018150 3.566
## humidity_max:DistrictKhammam -0.397150 0.019118 -20.774
## humidity_max:DistrictKumuram Bheem - Asifabad 0.127120 0.019009 6.687
## humidity_max:DistrictMahabubabad -0.145657 0.022138 -6.580
## humidity_max:DistrictMahabubnagar 0.007429 0.015174 0.490
## humidity_max:DistrictMancherial 0.230288 0.018429 12.496
## humidity_max:DistrictMedak 0.042453 0.015267 2.781
## humidity_max:DistrictMedchal-Malkajgiri -0.220198 0.018326 -12.015
## humidity_max:DistrictNagarkurnool -0.024717 0.016818 -1.470
## humidity_max:DistrictNalgonda -0.361243 0.015172 -23.810
## humidity_max:DistrictNirmal 0.101949 0.016224 6.284
## humidity_max:DistrictNizamabad -0.022474 0.014617 -1.538
## humidity_max:DistrictPeddapalli 0.102514 0.020469 5.008
## humidity_max:DistrictRajanna-Siricilla -0.028918 0.017454 -1.657
## humidity_max:DistrictRangareddy -0.052521 0.014759 -3.559
## humidity_max:DistrictSangareddy -0.029264 0.015161 -1.930
## humidity_max:DistrictSiddipet -0.067168 0.015769 -4.260
## humidity_max:DistrictSuryapet -0.370164 0.018929 -19.555
## humidity_max:DistrictVikarabad 0.002182 0.015519 0.141
## humidity_max:DistrictWanaparthy -0.006976 0.019260 -0.362
## humidity_max:DistrictWarangal (R) -0.011609 0.022884 -0.507
## humidity_max:DistrictWarangal (U) -0.013969 0.024034 -0.581
## humidity_max:DistrictYadadri-Bhongir -0.329670 0.018456 -17.862
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## humidity_max < 2e-16 ***
## DistrictBhadradri-Kothagudem 0.006983 **
## DistrictHyderabad 0.000424 ***
## DistrictJagtial < 2e-16 ***
## DistrictJangaon 8.89e-12 ***
## DistrictJayashankar-Bhupalpally < 2e-16 ***
## DistrictJogulamba-Gadwal 6.76e-06 ***
## DistrictKamareddy 2.98e-11 ***
## DistrictKarimnagar < 2e-16 ***
## DistrictKhammam < 2e-16 ***
## DistrictKumuram Bheem - Asifabad 1.13e-13 ***
## DistrictMahabubabad 0.027274 *
## DistrictMahabubnagar 5.16e-06 ***
## DistrictMancherial < 2e-16 ***
## DistrictMedak < 2e-16 ***
## DistrictMedchal-Malkajgiri 3.18e-14 ***
## DistrictNagarkurnool 0.005104 **
## DistrictNalgonda < 2e-16 ***
## DistrictNirmal < 2e-16 ***
## DistrictNizamabad 0.002926 **
## DistrictPeddapalli < 2e-16 ***
## DistrictRajanna-Siricilla 0.000529 ***
## DistrictRangareddy 0.451574
## DistrictSangareddy 0.013495 *
## DistrictSiddipet 0.051303 .
## DistrictSuryapet < 2e-16 ***
## DistrictVikarabad 4.90e-05 ***
## DistrictWanaparthy 0.046225 *
## DistrictWarangal (R) 0.000355 ***
## DistrictWarangal (U) 0.000278 ***
## DistrictYadadri-Bhongir < 2e-16 ***
## humidity_max:DistrictBhadradri-Kothagudem 0.105423
## humidity_max:DistrictHyderabad 1.54e-07 ***
## humidity_max:DistrictJagtial < 2e-16 ***
## humidity_max:DistrictJangaon < 2e-16 ***
## humidity_max:DistrictJayashankar-Bhupalpally 2.92e-06 ***
## humidity_max:DistrictJogulamba-Gadwal 8.77e-13 ***
## humidity_max:DistrictKamareddy 0.000199 ***
## humidity_max:DistrictKarimnagar 0.000363 ***
## humidity_max:DistrictKhammam < 2e-16 ***
## humidity_max:DistrictKumuram Bheem - Asifabad 2.28e-11 ***
## humidity_max:DistrictMahabubabad 4.73e-11 ***
## humidity_max:DistrictMahabubnagar 0.624423
## humidity_max:DistrictMancherial < 2e-16 ***
## humidity_max:DistrictMedak 0.005424 **
## humidity_max:DistrictMedchal-Malkajgiri < 2e-16 ***
## humidity_max:DistrictNagarkurnool 0.141654
## humidity_max:DistrictNalgonda < 2e-16 ***
## humidity_max:DistrictNirmal 3.31e-10 ***
## humidity_max:DistrictNizamabad 0.124163
## humidity_max:DistrictPeddapalli 5.49e-07 ***
## humidity_max:DistrictRajanna-Siricilla 0.097556 .
## humidity_max:DistrictRangareddy 0.000373 ***
## humidity_max:DistrictSangareddy 0.053584 .
## humidity_max:DistrictSiddipet 2.05e-05 ***
## humidity_max:DistrictSuryapet < 2e-16 ***
## humidity_max:DistrictVikarabad 0.888206
## humidity_max:DistrictWanaparthy 0.717182
## humidity_max:DistrictWarangal (R) 0.611937
## humidity_max:DistrictWarangal (U) 0.561095
## humidity_max:DistrictYadadri-Bhongir < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.07 on 230322 degrees of freedom
## Multiple R-squared: 0.4133, Adjusted R-squared: 0.4132
## F-statistic: 2660 on 61 and 230322 DF, p-value: < 2.2e-16qqnorm(residuals(interaction_model))
qqline(residuals(interaction_model))
plot(interaction_model, which = 1)