Example 2. Simple Linear Regression: TV Ratings Data

The station manager of a TV network was concerned about news show ratings. Is there a holdover effect from the show immediately preceding the news, i.e., was the rating for the news show at least partially dependent on the rating of the show preceding it, called the "lead-in" show? To assess this, a random sample of previous ratings was taken across regions and for various time points over the past 2 years. The response variable Y is the news show rating, while the predictor variable X is the lead show rating. The rating is an index ranging between 1 and 10.

Source: Chatterjee, S. and Price, B. (1991). Regression Analysis by Example. John Wiley & Sons: New York.

Table 2: Ratings of TV shows

 X       Y       X       Y      
2.50    3.80    5.50    4.35
2.70    4.10    5.70    4.15
2.90    5.80    5.90    4.85
3.10    4.80    6.10    6.20
3.30    5.70    6.30    3.80
3.50    4.40    6.50    7.00
3.70    4.80    6.70    5.40
3.90    3.60    6.90    6.10
4.10    5.50    7.10    6.50
4.30    4.15    7.30    6.10
4.50    5.80    7.50    4.75
4.70    3.80    2.50    1.00
4.90    4.75    2.70    1.20
5.10    3.90    7.30    9.50
5.30    6.20    7.50    9.00

Questions:

1. Does a linear regression appear to be reasonable fit?
   
   
2. Can we identify any anomalous observations? If so, do they affect the fitted regression? How?
   
   
3. How can such points be identified? How should such anomalous data be handled in the entire analysis?

Keywords: Outliers, ordinary residuals, standardized residuals, normalized residuals, internally and externally Studentized residuals.