Use least-squares regression to fit the following function to the given data and
ID: 3064201 • Letter: U
Question
Use least-squares regression to fit the following function to the given data and determine coefficients and :
y=x+x
Calculate the Least Squares Error of the model. Make a plot to show the data points (circle marker) vs fitted function (solid line). What is the best estimate of y for x = 1.45 using this function?
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clear
clc
x = 0.5:0.1:2;
y = [-17.19, -14.14, -12.51, -10.64, -9.34, -9.00, -7.81, -7.53, -6.49, -5.76, -5.62, -5.26, -4.78, -4.46, -4.41, -4.00];
scatter(x,y)
grid minor
Explanation / Answer
model= lm (y~x)
> summary(model)
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-3.4149 -0.7267 0.3322 1.0120 1.3920
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -17.5860 1.0073 -17.46 6.73e-11 ***
x 7.6218 0.7561 10.08 8.45e-08 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.394 on 14 degrees of freedom
Multiple R-squared: 0.8789, Adjusted R-squared: 0.8703
F-statistic: 101.6 on 1 and 14 DF, p-value: 8.455e-08
y^ = -17.586 + 7.6218 * x
when x = 1.45
y^ = -17.586 + 7.6218 *1.45
= -6.53439
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