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Find a regression equation.

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Average atmospheric levels of CO$_2$ in the 2000s (x) and 2010s (y) decades were recorded for ten locations (A-J) as reported in this table (in ppm units):

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Location	x	y
{obj[0]}	{r1[0]}	{r2[0]}
{obj[1]}	{r1[1]}	{r2[1]}
{obj[2]}	{r1[2]}	{r2[2]}
{obj[3]}	{r1[3]}	{r2[3]}
{obj[4]}	{r1[4]}	{r2[4]}
{obj[5]}	{r1[5]}	{r2[5]}
{obj[6]}	{r1[6]}	{r2[6]}
{obj[7]}	{r1[7]}	{r2[7]}
{obj[8]}	{r1[8]}	{r2[8]}
{obj[9]}	{r1[9]}	{r2[9]}

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Part a):

Excel:

copy the table on the spreadsheet: \"Ctrl-c\" making sure your cursor is displayed as \"I-beam\" (not as pointer/arrow);
click and hold to select the data (numbers only);
click on \"Insert | Charts | Scatter\" to plot the data;
right-click on any data point on the plot and select \"Add Trendline\";
select \"Display Equation on chart\" to obtain the linear model.

Minitab:

copy the table on the spreadsheet, with the labels \"Location (x) (y)\" in the first (grey) row;
click on \"Stat | Regression | Fitted Line Plot\";
enter Response and Predictor as appropriate.

For part b and c, as well as generally for the underlying theory of linear correlation and regression, check your learning material (e.g., Chapter 8 in OpenIntro Statistics).

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Use a spreadsheet or stats software to obtain the regression model $y = b_0 + b_1 \\times x$:

$b_0=\\;$[[0]]ppm

$b_1=\\;$[[1]]

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Using the model obtained above, calculate the predicted 2010s concentration for location $\\var{obj[ch]}$:

$CO_2^{\\,2010\\text{s}}=$ [[0]]ppm

Calculate $e_\\var{obj[ch]}$ (the residual for location $\\var{obj[ch]}$):

$e_\\var{obj[ch]}=$[[0]]ppm

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