R Lab: Linear Regression

# use this code chunk to call in all packages the document will need
library(tidyverse)
library(ssstats)

Tiny Tina, the explosive-loving Bunker Master, is hosting her first-ever Wonderlands Bake-Off. Contestants from across the realm, including goblins, skeletons, and glitter-loving orcs, are competing to craft the most delicious, magical baked treats.

Each contestant submits one dessert for judging. The judging panel includes:

• Tiny Tina, who values flair and sugar explosions,
• Butt Stallion, who insists on elegance and frosting symmetry, and
• Paladin Mike, who wants practical rations that still taste divine.

You, as the official Fateweaver Statistician, are tasked with determining what factors predict the panel’s overall satisfaction rating.

Each contestant records the following: - glitter_level: How much edible glitter was used (grams) - boom_factor: A subjective rating (1–10) of how explosive the dessert was - frosting_thickness: Thickness of frosting layer (mm) - overall_satisfaction: Combined score from all three judges (0–100 scale)

1. Construct a regression model that models overall satisfaction (overall_satisfaction) as a function of glitter level (glitter_level), boom factor (boom_factor), and frosting thickness (frosting_thickness). Remember to state your resulting regression model.

\hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x_1 +\ ...

2. Is this a significant regression line? Test at the \alpha=0.05 level. Remember to typeset your results.

• Hypotheses
  • H_0:
  • H_1:
• Test Statistic and p-Value
  • F_0 =; p =
• Rejection Region
  • Reject H_0 if p<\alpha; \alpha=
• Conclusion and Intepretation
  • Conclusion
  • Interpretation

3. Which, if any, are signficant predictors of overall satisfaction (overall_satisfaction)? Test at the \alpha=0.05 level. You do not need to formally write the hypothesis tests (i.e., typeset), but please provide a statement for each predictor, backed up statistically (using results generated).

• glitter_level: statement here (p =)

• boom_factor: statement here (p =)

• frosting_thickness: statement here (p =)

4a. Please provide a formal interpretation for glitter level (glitter_level).

Replace with your answer.

4b. Please provide a formal interpretation for boom factor (boom_factor).

Replace with your answer.

4c. Please provide a formal interpretation for frosting thickness (frosting_thickness).

Replace with your answer.

5. Please write a brief summary paragraph for Tiny Tina. Include information about your summary statistics, slope interpretations (you can be more general here – remember that she is 13 and not a statistician/data scientist), and test results (frame this as what matters most according to the model we constructed).

Replace with your answer.