Scientists are assessing if the CO2 concentration at a single location can be used to estimate the mean global annual temperature. The variables are x=CO2 concentration (in parts per 10°) at top of Mauna Loa in Hawaii and y3Dmean annual temperature in Celsius (over land and water across the globe). Consider the data for 1959--1995 (n=37 years); for example (x,y)=(2.452,16.53) in 1959 and (x,y)=(6.412,16.83) in 1995. Summary statistics are: a = 4.639, s, = 1.226, y = 16.621, s, = 0.098, ry = 0.508. Question (a) What are the slope B, and intercept B, of the least squares regression line for y as a function of æ? B1= 0.0406 Bo= 16.433 Question (b) What is the residual SD : ô = (n – 2)-1 ( - Bo - Bịa,)? Question (c) Suppose (xi, y;) are indexed by increasing year. Describe a residual plot to check if the residuals are serially correlated. Question (d) Assuming that the residual plot (c) is acceptable, what is a prediction interval for mean temperature of the globe when the CO2 concentration is 6.5 parts per 10°?

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Scientists are assessing if the CO2 concentration at a single location can be used to estimate the mean global annual temperature. The variables are X3CO2
concentration (in parts per 10°) at top of Mauna Loa in Hawaii and y=mean annual temperature in Celsius (over land and water across the globe). Consider the
data for 1959--1995 (n=37 years); for example (x,y)%3(2.452,16.53) in 1959 and (x,y)%3(6.412,16.83) in 1995. Summary statistics are:
* = 4.639, s, = 1.226, j = 16.621, s, = 0.098, rry = 0.508.
Question (a)
What are the slope B, and intercept B, of the least squares regression line for y as a function of x?
B= 0.0406
Bo= 16.433
Question (b)
What is the residual SD : ô =
V
(n – 2)-1 ( - Bo - B,2;)2?
Question (c)
Suppose (x;, yi) are indexed by increasing year. Describe a residual plot to check if the residuals are serially correlated.
Question (d)
Assuming that the residual plot (c) is acceptable, what is a prediction interval for mean temperature of the globe when the CO2 concentration is 6.5 parts per 10°?
Transcribed Image Text:Scientists are assessing if the CO2 concentration at a single location can be used to estimate the mean global annual temperature. The variables are X3CO2 concentration (in parts per 10°) at top of Mauna Loa in Hawaii and y=mean annual temperature in Celsius (over land and water across the globe). Consider the data for 1959--1995 (n=37 years); for example (x,y)%3(2.452,16.53) in 1959 and (x,y)%3(6.412,16.83) in 1995. Summary statistics are: * = 4.639, s, = 1.226, j = 16.621, s, = 0.098, rry = 0.508. Question (a) What are the slope B, and intercept B, of the least squares regression line for y as a function of x? B= 0.0406 Bo= 16.433 Question (b) What is the residual SD : ô = V (n – 2)-1 ( - Bo - B,2;)2? Question (c) Suppose (x;, yi) are indexed by increasing year. Describe a residual plot to check if the residuals are serially correlated. Question (d) Assuming that the residual plot (c) is acceptable, what is a prediction interval for mean temperature of the globe when the CO2 concentration is 6.5 parts per 10°?
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