Lab 4: Correlation and Regression Exercise 1 The percentage of babies born out of wedlock in the United States has increased steadily during the past few decades (see table below). The increase is due to a variety of factors, including an increase in the number of unplanned births, the existence of more alternative family units, and greater societal acceptance of single-parent households or couples that choose to have a child before getting married. Let x represent years since 1900 and y represent the percent of births out of wedlock in the U.S. Year Percent (%) of Births out of Wedlock 1970 10.7 1975 14.3 1980 18.4 1985 22.0 1990 28.0 1995 32.2 2000 33.2 a. Create and interpret a scatterplot for this data. In your interpretation, make sure you are discussing the four features outlined in class. b. Using your calculator, find Pearson's r and discuss if the two variables are significantly correlated. Explain how you determined this using the critical r-value as evidence. C. Using your calculator, find the slope of the resulting regression line. Interpret the slope. d. Using your resulting regression line, extrapolate when only 5% of births were out of wedlock. e. Create and interpret a residual plot for this data. In your interpretation, make sure you are discussing how well the data fits the linear modelExercise 2 During a 6-day period, Egan Electronics kept daily records of the number of assembly line workers absent and the number of defective parts produced. The information is provided in the following chart. Day 1 NUI Worker Abs. 3 Defects 15 22 12 20 30 a. Create and interpret a scatterplot for this data. In your interpretation, make sure you are discussing the four features outlined in class. b. Using your calculator, find Pearson's r and discuss if the two variables are significantly correlated. Explain how you determined this using the critical r-value as evidence. C. Using your calculator, find the slope of the resulting regression line. Interpret the slope. d. Using your resulting regression line, interpolate how many defects we can expect if 4 workers are absent. e. Create and interpret a residual plot for this data. In your interpretation, make sure you are discussing how well the data fits the linear model