Question
Do the data suggest a linear . quadratic or an exponential function ? Use regression to find a model for each data set.
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)
Hint:
1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. Regression is a statistical tool used to find a model that can represent the relation between a given change in dependent variable (
) for a given change in independent variable (
).
Linear Equation using regression can be represented as-
Y = a + bX, where-
a =![fraction numerator space left square bracket left parenthesis capital sigma y right parenthesis left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis space left parenthesis capital sigma x y right parenthesis right square bracket over denominator space left square bracket n left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis squared right square bracket end fraction](data:image/png;base64,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)
b =![fraction numerator space left square bracket n left parenthesis capital sigma x y right parenthesis space minus space left parenthesis capital sigma x right parenthesis space left parenthesis capital sigma y right parenthesis right square bracket over denominator space left square bracket n left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis squared right square bracket end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAAqCAYAAADbJjutAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAA/9JREFUeNrtXT1oFEEUHiQcEoKNhHBYBIKIhYhgISEEGxEJctiJhYgIQSRIClsRESFYXCF2IiIigkgKkSCIiISQRoKIlZDC0iaIiIQgnG/0CcM4s/v25m93533wQXZub/d9L9/szM5uXoSIiyvAJZEGS3j+lAipv6q+ELHUIceFOAxcTxzDGsbRVv1UfSFjCZbjgUKX4I5obdvasXXuAHd51HEUuJqwA4TWT9UXMhZTDD784/ZlFLxmaL+J4mJenVYxUTERU3+Zvhix2GJIasI7wAXLZ8+Bn4FjkQxxNcG8NKb+Mn0xYrHFEMSEN4DXgBPAh8CfwC0MQsUr4KzlGLuB74FPCs5/ySLqFn4m8QB41rDPIvC2sj0NfBPZhDH0U/W5xOKa4yAmfIaGkwY8jnOGfTi/GFX2+w7sFBy/C/wKvFiwzwaa/R/kvveU7QvYy1WMYs/eq7R1MJ6YiKGfqs8lFtccBzGhPPm8oX1LC+oX4RwngV+AI5bPTwH7+PMJQ0+bw06hX6mvG461E9mEMfRT9bnE4ppj7yaUV70fhvYRHJarCJ/A+chkyX6v8Yr7QTO5wO1PyvY4cBOHmGFNOCDQhwl96PdlwqJYXHPs3YTHgG8N7dOG9qIhYBLnIOOEOBZL7uBU8/dx/6rDVezh2Kd+1+GYEotLjr2b8BzOBSntsgfPGPY9BLxv6Uk6ZrCH9vEctqWBKeSmZV0rxY1JLP0Ufa6xuOTYuwnvGu7MbO2mZYHZCkslUvALnASP4R2caTh6BOxhbz5vOdaCYXKdYokmhH6KPtdYXHLs3YTLOFGltOsLpHMFa1U65NCwoiX9NPCxZbiSywgfS3py6sXqUPop+lxicc2xdxNuWS7dtvZ1ZS7zjTDh7yCXcdlHx1O8Y1RxBr/bs+hI+dguhn6qvmFi8ZHjpE9MhIjzAL9Xcg5+gcE9FpccO/loW6ELLouwj8xWcFJsmwvNi7QIqb+qvmFjGSbHvvxTe8i7u5eCwTlmMBiMRmPAZEYmg8FgMBgMBoPB0G7I5CtScrV/P6eEc5IK8pUk+YfbG5wKzomO2FUb1EdLXLXh/5xkh9hVG+Sr8++0ttxfejDlpHHziqZUbeji+aa09pyrNthy0pgF5yZVbTgg/j6Y71o+z7FqQ1lORA4mjFW1QCZZvp60p2Cf3Ko2UHLSaBPWqWqDwGQfLNGSW9UGSk4abcI6VW0QgvZgPbeqDdSXDRprwjpVbaiCnKs2tOpKWLeqDSFM2MaqDa0yYR2rNlCQe9WGVpmwjlUbKMi9akOrTFjHqg0U5F61oVUmrGPVBgpyr9rQKhPWsWpDGbhqQ8tMWBX8byfqU7WhkSZsStWGsnkZV20I97v9g99bE9JVoz3XIgAAAkx0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1vPiYjeEEwOzwvbW8+PG1vPls8L21vPjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPiYjeDNBMzs8L21pPjxtaT54PC9taT48bWk+eTwvbWk+PG1vPik8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4tPC9tbz48bW8+JiN4QTA7PC9tbz48bW8+KDwvbW8+PG1pPiYjeDNBMzs8L21pPjxtaT54PC9taT48bW8+KTwvbW8+PG1vPiYjeEEwOzwvbW8+PG1vPig8L21vPjxtaT4mI3gzQTM7PC9taT48bWk+eTwvbWk+PG1vPik8L21vPjxtbz5dPC9tbz48L21yb3c+PG1yb3c+PG1vPiYjeEEwOzwvbW8+PG1vPls8L21vPjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPiYjeDNBMzs8L21pPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4pPC9tbz48bW8+JiN4QTA7PC9tbz48bW8+LTwvbW8+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1yb3c+PG1vPig8L21vPjxtaT4mI3gzQTM7PC9taT48bWk+eDwvbWk+PG1vPik8L21vPjwvbXJvdz48bW4+MjwvbW4+PC9tc3VwPjxtbz5dPC9tbz48L21yb3c+PC9tZnJhYz48L21hdGg+ymblUQAAAABJRU5ErkJggg==)
The correct answer is: The given function is a linear function and using Regression, the given function can be modelled into the equation- Y = 2.48X - 19.96.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = 0, y1 = 100;
x2 = 1, y2 = 89.5;
x3 = 2, y3 = 78.9;
x4 = 3, y4 = 68.4;
x5 = 4, y5 = 57.8
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 1 - 0 = 1
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = 89.5 - 100 = -10.5
dy2 = y3 - y2 = 78.9 - 89.5 = -10.6
dy3 = y4 - y3 = 68.4 - 78.9 = -10.5
dy4 = y5 - y4 = 57.8 - 68.4 = -10.6
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is almost constant i.e. -10.5.
Hence, the given function is a linear function.
Using Linear Regression formula-
Y = a + bX, where-
a = ![fraction numerator left square bracket left parenthesis capital sigma y right parenthesis left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis space left parenthesis capital sigma x y right parenthesis right square bracket space over denominator left square bracket n left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis squared right square bracket end fraction](data:image/png;base64,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)
∴ a =
.......................... (As per adjacent table)
∴ a = ![fraction numerator left parenthesis negative 2 comma 250 space plus space 1 comma 252 right parenthesis over denominator space left parenthesis 150 space minus space 100 right parenthesis end fraction](data:image/png;base64,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)
∴ a =![fraction numerator space minus 998 space over denominator 50 end fraction](data:image/png;base64,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)
∴ a = -19.96
b = ![fraction numerator left square bracket n left parenthesis capital sigma x y right parenthesis space minus space left parenthesis capital sigma x right parenthesis space left parenthesis capital sigma y right parenthesis right square bracket space over denominator left square bracket n left parenthesis capital sigma x squared right parenthesis space minus space left parenthesis capital sigma x right parenthesis squared right square bracket end fraction](data:image/png;base64,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)
∴ b =![fraction numerator space left square bracket 5 left parenthesis negative 125.2 right parenthesis space minus space left parenthesis 10 right parenthesis left parenthesis negative 75 right parenthesis right square bracket over denominator space left square bracket 5 left parenthesis 30 right parenthesis space minus space left parenthesis 10 right parenthesis squared right square bracket end fraction](data:image/png;base64,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)
∴ b = (-626 + 750)/ (150 - 100)
∴ b = ![fraction numerator 124 over denominator space 50 end fraction](data:image/png;base64,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)
∴ b = 2.48
∴ The Linear Equation is-
Y = a + bX
∴ Y = -19.96 + 2.48X
∴ Y = 2.48X - 19.96
Final Answer:-
∴ The given function is a linear function and using Regression, the given function can be modelled into the equation- Y = 2.48X - 19.96.
x2 = 1, y2 = 89.5;
x3 = 2, y3 = 78.9;
x4 = 3, y4 = 68.4;
x5 = 4, y5 = 57.8
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 1 - 0 = 1
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = 89.5 - 100 = -10.5
dy2 = y3 - y2 = 78.9 - 89.5 = -10.6
dy3 = y4 - y3 = 68.4 - 78.9 = -10.5
dy4 = y5 - y4 = 57.8 - 68.4 = -10.6
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is almost constant i.e. -10.5.
Hence, the given function is a linear function.
Using Linear Regression formula-
Y = a + bX, where-
a =
∴ a =
∴ a =
∴ a =
∴ a = -19.96
b =
∴ b =
∴ b = (-626 + 750)/ (150 - 100)
∴ b =
∴ b = 2.48
∴ The Linear Equation is-
Y = a + bX
∴ Y = -19.96 + 2.48X
∴ Y = 2.48X - 19.96
Final Answer:-
∴ The given function is a linear function and using Regression, the given function can be modelled into the equation- Y = 2.48X - 19.96.