Levels of carbon dioxide (CO₂) in the atmosphere are rising rapidly, far above any levels ever before recorded. Levels were around 278 parts per million in 1800, before the Industrial Age, and had never, in the hundreds of thousands of years before that, gone above 300 ppm. Levels are now nearing 400 ppm. Table 2.35 shows the rapid rise of CO₂ concentrations over the last 50 years, also available in CarbonDioxide. We can use this information to predict CO₂ levels in different years.

Table 2.35

Year.........................CO₂
1960.....................316.91
1965.....................320.04
1970.....................325.68
1975.....................331.08
1980.....................338.68
1985.....................345.87
1990.....................354.16
1995.....................360.62
2000.....................369.40
200..................... 379.76
2010....................389.78

(a) What is the explanatory variable? What is the response variable?

(b) Draw a scatterplot of the data. Does there appear to be a linear relationship in the data?

(c) Use technology to find the correlation between year and CO₂ levels. Does the value of the correlation support your answer to part (b)?

(d) Use technology to calculate the regression line to predict CO₂ from year.

(e) Interpret the slope of the regression line, in terms of carbon dioxide concentrations.

(f) What is the intercept of the line? Does it make sense in context? Why or why not?

(g) Use the regression line to predict the CO₂ level in 2003. In 2020.

(h) Find the residual for 2010.