(a) Find the equation for the least-squares regression line for predicting CO2 emissions from highway fuel consumption:
The most common method for fitting a line to a scatterplot minimizes the sum of the squares of the vertical distances between the explanatory variable (highway fuel consumption) and the response variable (CO2 emissions). This method is known as least-squares regression.
To find the equation for the least-squares regression line, we can calculate the equation of the line that best fits the observed Y-values from the given data. Since CO2 emissions are the response variable and highway fuel consumption is the explanatory variable, we need to determine the equation that predicts CO2 emissions based on highway fuel consumption.
After determining that CO2 emissions represent the response variable and highway fuel consumption represents the explanatory variable, we can calculate the equation for the least-squares regression line.
The means and standard deviations of the sample are denoted by X-bar and Sx, respectively, and Y-bar and Sy, respectively. The correlation between the equation of the least-squares regression line and X is denoted by r, with slope b1 and intercept b0.
You can use software or a calculator with a regression function to find the equation of the least-squares regression line. The equation will be in the form Y = b0 + b1X, where b1 is the slope and b0 is the intercept. Make sure to round the slope to five decimal places and the intercept to five decimal places (0.4294).