Answer :
The least-squares line for the given data can be determined using linear regression analysis.
How can linear regression analysis be used to find the least-squares line for the given data?
Linear regression analysis is a statistical method used to model the relationship between a dependent variable (in this case, yield) and one or more independent variables (temperature). The goal is to find a linear equation that best fits the data points, minimizing the sum of the squared differences between the observed and predicted values. In the context of the given data, we want to find the equation of the least-squares line that represents the relationship between temperature (X) and yield (Y).
To find the equation of the least-squares line, we first calculate the correlation coefficient (r) between temperature and yield to determine the strength and direction of the relationship. Next, we calculate the slope (m) and intercept (b) of the line using the formulas:
m=r× S x/S y
b= yˉ −m× xˉ
Where S^y is the standard deviation of yield, S^x is the standard deviation of temperature, yˉ is the mean yield, and x ˉ is the mean temperature.
Once we have the slope and intercept, we can write the equation of the least-squares line as:
Y=mX+b
Using the provided data, perform the necessary calculations to find the values of m and b, then substitute them into the equation to obtain the least-squares line that best fits the data points.
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