a) Write out the model for the simple linear regression. Define all terms used in the model. b) What are the values of the intercept and the slope of the regression equation? c) Write out the regression equation.

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The paired data below show the Coursework marks of 6 randomly selected students from a statistics course at UWI and
their Final Exam marks in the same course.
Coursework Mark, x
Final Exam Mark, y
> x <-c(27, 28, 12, 41, 33, 9)
>y<-c(22, 34, 17, 45, 33, 16)
>result <- lm (y x)
> summary (result).
Call:
1m (formula y x)
Residuals:
1
A
27
22
B
28
34
A linear regression equation was found using R, and the output is shown below.
2
3
4
-7.5563 3.5822 0.3659 3.3830 -1.7252 1.9509
Student
Coefficients:
Estimate Std. Error t value Pr (>t|)
(Intercept) 6.2964 4.6774 1.346 0.24949
0.1706 5.048 0.00724 **
0.8615
C
с
12
17
D
41
45
Signif. codes: 0 **** 0.001 **0.01 0.05 0.11
Residual standard error: 4.698 on 4 degrees of freedom
Multiple R-squared: 0.8643, Adjusted R-squared: 0.8304
F-statistic: 25.49 on 1 and 4 DF, p-value: 0.007239
E
33
33
F
9
16
a) Write out the model for the simple linear regression. Define all terms used in the model.
b) What are the values of the intercept and the slope of the regression equation?
c) Write out the regression equation.
d) A UWI student in this Mathematics course obtains a coursework mark of 30. What is the best predicted value of their
Final Exam mark?
e) Should this regression equation be used to predict the test score of a UWI student in this Mathematics course who
obtains a coursework mark of 49? Explain briefly.
Transcribed Image Text:The paired data below show the Coursework marks of 6 randomly selected students from a statistics course at UWI and their Final Exam marks in the same course. Coursework Mark, x Final Exam Mark, y > x <-c(27, 28, 12, 41, 33, 9) >y<-c(22, 34, 17, 45, 33, 16) >result <- lm (y x) > summary (result). Call: 1m (formula y x) Residuals: 1 A 27 22 B 28 34 A linear regression equation was found using R, and the output is shown below. 2 3 4 -7.5563 3.5822 0.3659 3.3830 -1.7252 1.9509 Student Coefficients: Estimate Std. Error t value Pr (>t|) (Intercept) 6.2964 4.6774 1.346 0.24949 0.1706 5.048 0.00724 ** 0.8615 C с 12 17 D 41 45 Signif. codes: 0 **** 0.001 **0.01 0.05 0.11 Residual standard error: 4.698 on 4 degrees of freedom Multiple R-squared: 0.8643, Adjusted R-squared: 0.8304 F-statistic: 25.49 on 1 and 4 DF, p-value: 0.007239 E 33 33 F 9 16 a) Write out the model for the simple linear regression. Define all terms used in the model. b) What are the values of the intercept and the slope of the regression equation? c) Write out the regression equation. d) A UWI student in this Mathematics course obtains a coursework mark of 30. What is the best predicted value of their Final Exam mark? e) Should this regression equation be used to predict the test score of a UWI student in this Mathematics course who obtains a coursework mark of 49? Explain briefly.
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