Class Activity #6

Below are the close prices and highest prices (next day) of a stock in NASDAQ:

Close price, x	27.94	26.75	26.19	27.19	26.69	27.87	37.06	36.81	36.38	33.50	31.44	33.25
High price (next day), y	27.38	27.44	26.81	27.50	28.13	28.44	39.38	37.06	36.13	34.63	33.88	33.63

1. Use the TI-83 to help you construct the scatterplot.
2. Describe the overall pattern. Is there an outlier?
3. Based on the scatterplot, do you expect the correlation to be positive or negative? near ±1 or not?
4. Compute the correlation r.
5. What percent of the observed variation in the highest price is explained by a straight–line relationship with the close price?
6. Predict the highest price tomorrow if the close price today is $20.

Adapted from http://www.uoregon.edu/~qmshao/fall98/243ch2.pdf

ANSWERS:

1. Here is the scatterplot:
   
2. The pattern seems to be strongly linear. There does not seem to be any outliers.
3. Based on the scatterplot, I expect the correlation to be positive and near +1.
4. r = 0.98.
5. 96% (r² = 0.95) percent of the observed variation in the highest price is explained by a straight–line relationship with the close price.
6. The general linear regression line is: . The linear regression model for this data is: = 1.03 x – 0.17. Thus, the predicted highest price tomorrow if the close price today is $20 would be: = 1.03 (20) – 0.17 = $20.44.