Climate change 2013 Data collected from around the globe...

Climate change 2013 Data collected from around the globe show that the earth is getting warmer. The most common theory relates climate change to an increase in atmospheric levels of carbon dioxide $\left(\mathrm{CO}_{2}\right)$, a greenhouse gas. The mean annual $\mathrm{CO}_{2}$ concentration in the atmosphere (parts per million) is measured at the top of Mauna Loa in Hawaii (away from any local contaminants) and available at ftp://aftp.cmdl.noaa.gov /products/trends/co2/co2_annmean_mlo.txt The mean surface air temperature is recorded as the change in ${ }^{\circ} \mathrm{C}$ relative to a base period of 1951 to $1980 .$ It is available at data.giss.nasa.gov/gistemp/graphs_v3/ Here are a scatterplot and regression for the years from 1970 to 2013: Response variable is Global Avg Temp R-squared $=73.6 \% \quad$ R-squared (adjusted) $=72.9 \%$ $s=0.1316$ with $44-2=42$ degrees of freedom $\begin{array}{lcccl}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & 10.6442 & 0.3418 & 31.1 & \leq 0.0001 \\ \mathrm{C} 0_{2} & 0.010325 & 0.0010 & 10.8 & \leq 0.0001\end{array}$ a) Write the equation of the regression line. b) Is there evidence of an association between $\mathrm{CO}_{2}$ level and global temperature? c) Do you think predictions made by this regression will be very accurate? Explain. d) Does this regression prove that increasing $\mathrm{CO}_{2}$ levels are causing global warming? Discuss.

Climate change 2013 Data collected from around the globe show that the earth is getting warmer. The most common theory relates climate change to an increase in atmospheric levels of carbon dioxide $\left(\mathrm{CO}_{2}\right)$, a greenhouse gas. The mean annual $\mathrm{CO}_{2}$ concentration in the atmosphere (parts per million) is measured at the top of Mauna Loa in Hawaii (away from any local contaminants) and available at ftp://aftp.cmdl.noaa.gov /products/trends/co2/co2_annmean_mlo.txt
The mean surface air temperature is recorded as the change in ${ }^{\circ} \mathrm{C}$ relative to a base period of 1951 to $1980 .$ It is available at data.giss.nasa.gov/gistemp/graphs_v3/
Here are a scatterplot and regression for the years from 1970 to 2013: Response variable is Global Avg Temp R-squared $=73.6 \% \quad$ R-squared (adjusted) $=72.9 \%$ $s=0.1316$ with $44-2=42$ degrees of freedom
$\begin{array}{lcccl}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-Ratio } & \text { P-Value } \\ \text { Intercept } & 10.6442 & 0.3418 & 31.1 & \leq 0.0001 \\ \mathrm{C} 0_{2} & 0.010325 & 0.0010 & 10.8 & \leq 0.0001\end{array}$
a) Write the equation of the regression line.
b) Is there evidence of an association between $\mathrm{CO}_{2}$ level and global temperature?
c) Do you think predictions made by this regression will be very accurate? Explain.
d) Does this regression prove that increasing $\mathrm{CO}_{2}$ levels are causing global warming? Discuss.

Key Concepts

Simple Linear Regression

Simple linear regression is a statistical method used to model the relationship between two continuous variables by fitting a straight line through the data. The method estimates an intercept and a slope that best describe how changes in one variable predict changes in the other, allowing for both understanding and prediction of the response variable based on the predictor.

Interpretation of Regression Coefficients

The regression coefficients in a simple linear model include an intercept and a slope. The intercept represents the expected value of the response variable when the predictor is zero, while the slope indicates the amount by which the response variable is expected to change for a one-unit increase in the predictor. This interpretation helps in understanding the nature and strength of the relationship between the variables.

Statistical Significance and Hypothesis Testing

This concept involves using statistical tests, such as the t-test, to determine whether there is sufficient evidence to conclude that a relationship exists between the predictor and the response variable. P-values and confidence intervals are commonly used to assess whether the observed effects are statistically significant, helping to decide if the relationship is likely not due to random chance.

Association Versus Causation

It is important to distinguish between association and causation in statistical analysis. While regression may show a strong relationship between two variables (association), it does not on its own prove that changes in one variable cause changes in the other. Establishing causality typically requires additional experimental or longitudinal evidence to rule out confounding factors and alternative explanations.

Model Fit and Predictive Accuracy

Measures such as R-squared and adjusted R-squared are used to assess how well a regression model fits the data, indicating the proportion of variability in the response variable that is explained by the predictor. However, even a model with a good fit may have limitations when making predictions, especially when extrapolating beyond the range of observed data or when other unaccounted factors influence the response.

Transcript

00:01 Data collected from around the globe show that the earth is getting warmer, the most common theory relates climate change to an increase in atmosphere levels of carbon dioxide, a greenhouse gas.

00:10 The mean annual co2 concentration in the atmosphere is measured at the top of mauna loa in hawaii and available at the website.

00:22 The mean surface air temperature is recorded as a change in degrees celsius relative to a base period of 1951 to 1980.

00:31 It is available at the given website.

00:34 Here are a scatterplot and regression for the years from 1970 to 2013.

00:39 The response variable is global average temperature.

00:46 I want to write the equation of the regression line.

00:50 Notice that the y intercept is in the row co2 with the coefficient se coefficient standard error, so that is 0 .0010.

01:04 And then our slope would be the coefficient for co2, which would be 0 .030325.

01:29 And that would be our equation.

01:36 Part b, is there evidence of an association between co2 and global temperature? given the claim is that the slope is non -zero because there is an association? the null hypothesis would be that the slope is 0, and the alternate is that it is not.

02:00 And if you look at the p value, we get p is less than or equal to .0001, which is far less than 0 .05, which means we can reject the null hypothesis, meaning there is sufficient evidence to support the claim...

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