AE 21: Sesame Street

Multinomial logistic regression

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• STA 240: Probability for Statistical Inference, Modeling, and Data Analysis.
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  • Pre-req: STA 210, STA 230 or 240, CS 101 (or equivalent), multivariable calc
  • Co-req: Linear algebra

Project draft - due Oct 28

• Write the draft in the written-report.Rmd file in the project repo.
• Draft should include
  • exploratory data analysis
  • initial model selection (main effects + interactions)
  • initial interpretations / conclusions from model

Sesame Street

Today’s data comes from an experiment by the Educational Testing Service to test the effectiveness of the children’s program Sesame Street. Sesame Street is an educational program designed to teach young children basic educational skills such as counting and the alphabet

As part of the experiment, children were assigned to one of two groups: those who were encouraged to watch the program and those who were not.

The show is only effective if children watch it, so we want to understand what effect the encouragement had on the frequency children watched the program.

Response:

• viewcat
• 1: rarely watched show
• 2: once or twice a week
• 3: three to five times a week
• 4: watched show on average more than five times a week

Predictors:

• age: child’s age in months
• prenumb: score on numbers pretest (0 to 54)
• prelet: score on letters pretest (0 to 58)
• viewenc: 1: encouraged to watch, 0: not encouraged
• site:
  • 1: three to five year old from urban area
  • 2: four year old from suburban area
  • 3: from rural area with high socioeconomic status
  • 4: from rural area with low socioeconomic status
  • 5: from Spanish speaking home

Exploratory data analysis

1. Create a plot to visualize the relationship between the response and viewenc, the primary variable of interest in this analysis. What do you observe from the plot?

2. Create a plot to visualize the relationship between the response and a quantitative predictor variable. What do you observe from the plot?

Model selection

3. Fit a model with all predictors except the primary variable of interest, viewenc.

4. Conduct backward model selection using the step function and AIC as the model selection criterion. Display the chosen model.

Interpretation + conclusions

5. Interpret the intercept associated with the odds of a child being in the category viewcat == 2 versus viewcat == 1.

6. Interpret the coefficient of one numeric predictor in terms of the odds of a child being in the category viewcat == 2 versus viewcat == 1. Based on the confidence interval for the coefficient, is the numeric predictor a statistically significant predictor of viewership?

7. The primary objective of the experiment was to understand the effect of encouragement viewenc on viewership. Does encouragement have a significant effect on viewership after adjusting for other possible factors? If so, describe the effect. Otherwise, explain why not.