Snail Water Content Analysis: Investigating the Impact of Humidity and Temperature

This dataset contains percentage water content of snail tissues grown under three different levels of relative humidity and two different temperatures. We aim to analyze the relationship between water content and these environmental factors using linear regression.

First, we fit a full model including both temperature (temp) and humidity (humid) as predictors:

fullmod <- lm(water ~ temp + humid, data = snail)
summary(fullmod)

The output reveals a statistically significant effect of humidity (p-value = 5.63e-09) indicating a strong positive correlation between humidity and water content. However, temperature does not show a significant effect (p-value = 0.427).

Next, we fit a reduced model with only an intercept term:

red_mod <- lm(water ~ 1, data = snail)
summary(red_mod)

This model provides a baseline comparison to assess whether the full model offers significant improvement.

To determine whether the reduced model could be used instead of the full model, we perform a hypothesis test comparing the sum of squared errors (SSE) between the two models.

The null hypothesis (H0) is that the reduced model is sufficient, while the alternative hypothesis (Ha) is that the full model is necessary.

We calculate the F-statistic using the following formula: F = ((SSEr - SSEF) / (dfr - dff)) / (SSEF / dff)

where:

• SSEr = sum of squared errors for the reduced model* SSEF = sum of squared errors for the full model* dfr = degrees of freedom for the reduced model* dff = degrees of freedom for the full model

Given that SSEF = 3386.5 and SSER = 646.1, with dfr = 1 and dff = 21, we calculate the F-statistic:

F = ((646.1 - 3386.5) / (1 - 21)) / (3386.5 / 21)

Simplifying the equation, we get F = 0.85.

To determine the significance of this F-statistic, we compare it to the critical value from the F-distribution with degrees of freedom (1, 21). If the calculated F-statistic is greater than the critical value, we reject the null hypothesis and conclude that the full model is necessary. If the F-statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that the reduced model is sufficient.

This analysis highlights the importance of examining the relationship between water content in snails and environmental factors like humidity and temperature. The results suggest that humidity plays a significant role in determining water content, while temperature does not appear to have a strong influence. Further investigation with a larger dataset or different experimental conditions could provide a more comprehensive understanding of these complex relationships.