Question 1: Fill in the commands to load the packages ‘mosaic’, ‘Lock5withR’, ‘lattice’.

Answer: GO to packages and selct masaic and lock 5 with r

Question 2: Does a correlation coefficient of 0 mean the variables are not related? Is it possible to create the graph of a bivariate data set in which the variables are obviously related and the value of r is approximately equal to 0? Explain.

Answer: a correlation coefficient of 0 does not always mean there is no correlation between the two variables but rather says that there is no linear correlation between the variables. this means that if you create a graph that displays a parabolic correlation that is symetric, then then the correlation coefficient will come out zero.

Question 3: Level of carbon dioxide (\(CO_2\)) in the atmosphere are rising rapidly, far above any levels ever before recorded. Levels were around 278 parts per million 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. The following tabale shows the rapid rise of \(CO_2\) concentrations over the last 50 years.
Year | \(CO2\) —–|——— 1960 | 316.91
1965 | 320.04
1970 | 325.68
1975 | 331.08
1980 |
1985 | 345.87
1990 | 354.16
1995 | 360.62
2000 | 369.40
2005 | 379.76 2010 | 389.78

  1. Determine the explanatory and response variables

Answer: The explanatory variable is the number of years from 1960 while the res

  1. Produce a scatterplot of the data. Does there appear to be a linear relationship in the data?

Answer: Yes there appears to be a linear relationship in the data

  1. Find the correlation between the year and \(CO_2\) levels. Does the value of the correlation support your answer in the previous part? Explain.

Answer: Yes there is a strong correlation shown by a r value of .993 which is very close to perfect

  1. Calculate the regression line to predict \(CO_2\) from a given year.

Answer: for years after at or after 1960 y=1.471x-2571.212

  1. Interpret the slope of the regression line, in the context of carbon dioxide concentrations.

Answer: The line means that after 1960 every year the co2 concentration rises by 1.471

  1. What is the intercept of the line? Does it make sense in context? Why or why not?

Answer: the intercept of the line is -2571.212 which doesn’t make sense because you cant have negative co2 conccentrations. To make the dat useful we would have to turn the years into number of years after 1960

  1. Use the regression line to predict the \(CO_2\) level in 2003 and 2010.

Answer: For 2003 the co2 level is predicted to be 375.201 and in 2010 it is predicted to be 385.498

  1. Find the residual for 2010. the residual is 4.282