DataDiveten
2026-03-30
Data Dive Ten
GLMs
Load library
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## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)Load NASA data
nasa_data <- read_delim("C:/Users/imaya/Downloads/cleaned_5250.csv",delim = ",")## Rows: 5250 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (5): name, planet_type, mass_wrt, radius_wrt, detection_method
## dbl (8): distance, stellar_magnitude, discovery_year, mass_multiplier, radiu...
##
## 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.head(nasa_data)## # A tibble: 6 × 13
## name distance stellar_magnitude planet_type discovery_year mass_multiplier
## <chr> <dbl> <dbl> <chr> <dbl> <dbl>
## 1 11 Coma… 304 4.72 Gas Giant 2007 19.4
## 2 11 Ursa… 409 5.01 Gas Giant 2009 14.7
## 3 14 Andr… 246 5.23 Gas Giant 2008 4.8
## 4 14 Herc… 58 6.62 Gas Giant 2002 8.14
## 5 16 Cygn… 69 6.22 Gas Giant 1996 1.78
## 6 17 Scor… 408 5.23 Gas Giant 2020 4.32
## # ℹ 7 more variables: mass_wrt <chr>, radius_multiplier <dbl>,
## # radius_wrt <chr>, orbital_radius <dbl>, orbital_period <dbl>,
## # eccentricity <dbl>, detection_method <chr>Creating a Binary Variable
nasa_data_clean <- nasa_data |>
drop_na(eccentricity, stellar_magnitude, planet_type)
top_method <- nasa_data_clean %>% count(detection_method, sort =TRUE) %>% slice_head(n=1)
print(top_method)## # A tibble: 1 × 2
## detection_method n
## <chr> <int>
## 1 Transit 3943nasa_data_clean$Transit <- ifelse(nasa_data_clean$detection_method == "Transit", 1, 0)The detection method was converted into a binary variable indicating whether a planet was discovered using the transit method (1) or another method (0). The transit method was chosen as the reference category because it has identified over 75% of known exoplanets (Exoplanet Detection Methods | The Schools’ Observatory, 2023). This method detects planets when they pass in front of their host star, causing a periodic dip in the observed light. Below is an image from Exoplanet Detection Methods illustrating how the transit method works.
Reference
Exoplanet Detection Methods | The Schools’ Observatory. (2023). Schoolsobservatory.org. https://www.schoolsobservatory.org/learn/space/exoplanets/detection-methods
Logistic Regression Model
I built a logistic regression model to explore how orbital eccentricity, stellar magnitude, and planet type influence the likelihood that an exoplanet is detected using the Transit method.
model <- glm(Transit ~ eccentricity + stellar_magnitude + planet_type, data = nasa_data_clean, family =binomial)
summary(model)##
## Call:
## glm(formula = Transit ~ eccentricity + stellar_magnitude + planet_type,
## family = binomial, data = nasa_data_clean)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.47026 0.26618 -24.308 < 2e-16 ***
## eccentricity -4.33143 0.38449 -11.265 < 2e-16 ***
## stellar_magnitude 0.65887 0.02339 28.169 < 2e-16 ***
## planet_typeNeptune-like 0.79374 0.12711 6.245 4.25e-10 ***
## planet_typeSuper Earth 1.30399 0.15797 8.254 < 2e-16 ***
## planet_typeTerrestrial 2.17998 0.49528 4.402 1.07e-05 ***
## planet_typeUnknown -17.90729 364.43246 -0.049 0.961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5429.0 on 5088 degrees of freedom
## Residual deviance: 2274.8 on 5082 degrees of freedom
## AIC: 2288.8
##
## Number of Fisher Scoring iterations: 13coef(summary(model))## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.4702557 0.26617896 -24.30791618 1.616703e-130
## eccentricity -4.3314323 0.38449097 -11.26536804 1.945374e-29
## stellar_magnitude 0.6588730 0.02339034 28.16859753 1.418510e-174
## planet_typeNeptune-like 0.7937405 0.12710806 6.24461190 4.248537e-10
## planet_typeSuper Earth 1.3039944 0.15797486 8.25444241 1.526130e-16
## planet_typeTerrestrial 2.1799827 0.49527548 4.40155594 1.074774e-05
## planet_typeUnknown -17.9072869 364.43246436 -0.04913746 9.608097e-01The logistic regression shows that stellar magnitude has a positive coefficient (0.659). Stellar magnitude measures the brightness of a star, where higher values mean dimmer stars. The positive coefficient indicates that as stellar magnitude increases, the probability of detecting a planet via the Transit method also increases. This may be due to observational biases or the way Transit detections are measured.
Eccentricity has a negative coefficient (-4.33). Eccentricity measures how elliptical a planet’s orbit is, with 0 being a perfect circle. The negative coefficient suggests that planets with more elliptical orbits are less likely to be detected via Transit, likely because circular orbits increase the chance that a planet crosses directly in front of its star from our line of sight.
Planet type also influences detection. The model compares different types of planets to Gas Giants, which are the reference category. Neptune-like, Super Earth, and Terrestrial planets have positive coefficients, meaning they are more likely to be detected via Transit than Gas Giants. Gas Giants do not appear with a separate coefficient because they are the baseline for comparison. Different planet sizes and compositions affect how easily they block their star’s light when using the transit detection method.
exp(coef(model))## (Intercept) eccentricity stellar_magnitude
## 1.548830e-03 1.314870e-02 1.932613e+00
## planet_typeNeptune-like planet_typeSuper Earth planet_typeTerrestrial
## 2.211654e+00 3.683982e+00 8.846154e+00
## planet_typeUnknown
## 1.670952e-08Exponentiating the logistic regression coefficients gives odds ratios. The exponentiated intercept (0.00155) represents the baseline odds of detecting a planet via the transit method when all predictors are zero. Eccentricity has an odds ratio of 0.013, indicating that planets with more elliptical orbits are much less likely to be detected. Stellar magnitude has an odds ratio of 1.93, suggesting that higher magnitude stars are associated with increased detection odds; however, this result is counterintuitive and may reflect dataset bias or variable coding. Planet type also influences detection: Neptune-like, Super Earth, and Terrestrial planets have higher odds of detection compared to Gas Giants
Build Confidence Level
coef_stella <- coef(summary(model))["stellar_magnitude", "Estimate"]
se_stella <- coef(summary(model))["stellar_magnitude", "Std. Error"]
ci_low <- coef_stella - (1.96 * se_stella)
ci_up <- coef_stella + (1.96 * se_stella)
exp(c(ci_low,ci_up))## [1] 1.846013 2.023276The 95% confidence interval for the odds ratio of stellar magnitude is 1.85 to 2.02. This means we are 95% confident that this interval captures the true odds ratio. For each 1-unit increase in stellar magnitude, the odds of detecting a planet via the transit method increase by approximately 85% to 102%. However, since higher stellar magnitude corresponds to dimmer stars, this result may reflect dataset bias.