Question

Researchers measured the global mean temperatures (in degrees C) of the earth's surface every five years between 1950 and 2005. The data is listed below where the variable year is re-coded as follows: 1950 is coded as 1, 1955 as 2, and so on. Year 1 2 3 4 5 6 7 8 9 10 11 12 T (degC) 13.8 13.9 14.0 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4 14.8 a. Fit a simple linear regression model to the data using temperature as a response variable and year as an explanatory variable. b. Fit a third order polynomial regression model. c. Which model fits the data better? Sketch the both regression curves with the measured data. d. Use the model from (c) to enter the predicted global mean temperature for the year 1960

          Researchers measured the global mean temperatures (in degrees C) of the earth's surface every five years between 1950 and 2005. The data is listed below where the variable year is re-coded as follows: 1950 is coded as 1, 1955 as 2, and so on.

Year 1 2 3 4 5 6 7 8 9 10 11 12
T (degC) 13.8 13.9 14.0 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4 14.8

a. Fit a simple linear regression model to the data using temperature as a response variable and year as an explanatory variable.
b. Fit a third order polynomial regression model.
c. Which model fits the data better? Sketch the both regression curves with the measured data.
d. Use the model from (c) to enter the predicted global mean temperature for the year 1960

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Researchers measured the global mean temperatures (in degrees C) of the earth's surface every five years between 1950 and 2005. The data is listed below where the variable year is re-coded as follows: 1950 is coded as 1, 1955 as 2, and so on.

Year 1 2 3 4 5 6 7 8 9 10 11 12
T (degC) 13.8 13.9 14.0 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4 14.8

a. Fit a simple linear regression model to the data using temperature as a response variable and year as an explanatory variable.
b. Fit a third order polynomial regression model.
c. Which model fits the data better? Sketch the both regression curves with the measured data.
d. Use the model from (c) to enter the predicted global mean temperature for the year 1960

Added by Mark C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

05/30/2023

Step 1

First, we need to find the simple linear regression model. The equation for a simple linear regression model is $y = a + bx$, where $y$ is the temperature, $x$ is the coded year, and $a$ and $b$ are the coefficients we need to find. Show more…

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Researchers measured the global mean temperatures (in degrees C) of the earth's surface every five years between 1950 and 2005. The data is listed below where the variable year is coded as follows: 1950 is coded as 1, 1955 as 2, and so on. Year 1 2 3 4 5 6 7 8 9 10 11 12 T (degC) 13.8 13.9 14.0 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4 14.8 a. Fit a simple linear regression model to the data using temperature as a response variable and year as an explanatory variable. b. Fit a third order polynomial regression model. c. Which model fits the data better? Sketch the both regression curves with the measured data. d. Use the model from (c) to enter the predicted global mean temperature for the year 1960

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00:05 In this question, we first need to find the simple linear regression model.

00:10 So the equation for simple linear regression model, for simple linear regression model, the equation is y is equals to a plus x.

00:35 Now where y is the temperature, x is the coded year and a and b are the coefficient we needed.

00:42 So now next we need to fit a third order polynomial regression model.

00:50 So the equation, the equation for third order polynomial, third order polynomial regression model, that is we have y is equals to a plus bx plus cx square plus bx cube where y is the temperature, x is the year, coded year and a, b, c are the coefficient.

01:44 We needed to find now to determine which model fits the data better, we can compare r square values on both.

01:51 So what we will do, we will compare r square value of both model.

02:10 So higher the r square value, the better is the model fits.

02:14 So we can use the better fitting model to predict the global mean temperature for year what? for year 1960.

02:28 So we can calculate the coefficient for both the model to find the following equation.

02:34 So simple linear regression model equation is what? so y is equals to 13 .5 plus we have 0 .1x.

02:46 So the third order polynomial regression, this is the linear one and the third order, the third order equation is y is equals to 13 .4 plus we have 0 .15x plus we have, this is negative value so this will become minus 0 .01x square plus we have 0 .0002x cube...

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