Question

The accompanying scatto plot shows the regression line, 95% confidence interval, and 95% prediction interval for youth unemployment data for a sa The response variable is the Female Rate and the predictor variable is the Male Rate. a) Explain the meaning of the 95% prediction interval in this context. b) Explain the meaning of the 95% confidence interval in this context. c) Using a statistics program, identify any unusual observations, and discuss their potential impact on the regression. Click the icon to view the scatterplot for the youth unemployment data. pla o 20 nat s unemployment rate for a country given a a) The 95% prediction interval shows the interval of uncertainty for b) The 95% confidence interval shows the interval of uncertainty for V unemployment rate for a country given a c) Are there any unusual observations? O A There is an outlier. For this country, the female rate is much lower than the male rate. O B. There are several outliers. For these countries, the male and female rates are very different. O C. There is an outlier. For this country, the male rate is much lower than the female rate. O D. There are no unusual observations. What is the potential impact of any outliers on the regression? O A. Including any outliers would produce a stronger model. O B. Including any outliers would produce a weaker model. OC. Including any outliers would violate the Independence Condition, making the regression invalicd O D. Including any outliers would violate the Randomization Condition, making the regression invalid. 14 INFERENCE FOR REGRESSI 4 of 5 (0 complete) d 95%,prediction in erva foryouth unemploy ression line.95%,confidence interval, an Scatterplot for Youth Unemployment Data Youth Unemployment Rates 70- 60- 40 201 o-f 0 10 20 30 40 50 60 70 Male Rate s ーRegression S 95% Cl R-Sq 51.1% 95% Pl R-Sq(adj) 48.4% 5.2229 Print Done

Answer 1

Since the regression model is constructed to predict the Female unemployment rate (Response variable) using the Male unemployment rate (Predictor). Hence,

a) The 95% Prediction interval shows the interval of uncertainty for predicted female unemployment rate for a country given a male unemployment rate.

b) The 95% Confidence interval shows the interval of uncertainty for average female unemployment rate for a country given a male unemployment rate.

c) From the scatterplot for Youth unemployment data,

We find that the datapoint corresponding to female rate (approximately 40) and male unemployment rate (approximately 42) lies outside the 95% interval,way beyond the interval of uncertainty; hence can be considered as an unusual observation.Hence, the correct option would be:

There is a outlier. For this country, male rate is much lower than the female rate. For male rate, 40, according to the fitted model, the expected female rate would be near 20, however, the actual female rate is much higher.

Including the outlier, which being influential, would shift the regression line towards it. Since, the outlier lies far away from the rest, it would also increase the variance of the model, thus weakening it.Hence, including any outlier produces a weaker model.