Question

A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.

Test Scores

Student	First Test Grade	Second Test Grade
1	88	76
2	72	69
3	80	74
4	44	64
5	71	77
6	50	66
7	98	86
8	78	78
9	73	78
10	50	62
11	65	71
12	43	56
13	61	64
14	71	71
15	88	80
16	87	82
17	84	82
18	85	83
19	40	60
20	87	78
21	41	59

Step 1 of 2 :  

Using statistical software, estimate the parameters of the model

Second Test Grade=β0+β1(First Test Grade)+εi.

Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

Yi=______________+(________________)Xi

Answer 1

F
RGui (32-bit) - [R Console) R File Edit View Misc Packages Windows Help > x=c(88,72,80,44,71,50,98,78,73,50,65, 43,61,71,88,87,84,85, 40, 87, 41) > n=length(x) > n [1] 21 > y=c(76,69,74,64,77,66,86, 78, 78, 62, 71,56,64,71, 80, 82, 82, 83, 60, 78,59) >n=length(y) > n [1] 21 >> d-data.frame (x, y) d AN00 1 88 76 2 72 69 3 80 74 4 44 64 5 71 77 6 50 66 7 98 86 8 78 78 9 73 78 10 50 62 11 65 71 12 43 56 13 61 64 14 71 71 15 88 80 16 87 82 17 84 82 18 8583 19 40 60 20 87 78 21 41 59

> model=lm (yºx, data=d) > model Call: ln (formula = y - x, data = d) Coefficients: (Intercept) 40.4489 0.4578 > summary (model) Call: im (formula = y - x, data = d) Residuals: Min 10 Median -4.7363 -2.2785 0.6856 30 2.6605 Max 4.1309 Coefficients: Estimate Std. Erront value Pr(it) (Intercept) 40.44889 2.72289 14.86 6.53e-12 0.45781 0.03804 12.04 2.47e-10 *** Signif. codes: O "***" 0.001 **+ 0.01 N* 0.05 . 0.1 Residual standard error: 3.103 on 19 degrees of freedom Multiple R-squared: 0.884, Adjusted R-squared: 0.8779 F-statistic: 144.8 on 1 and 19 DE, p-value: 2.465e-10
Here we use R software

Independent Variable X : First test Grade.

DepedDepe Variable Y : Second test Grade.

From Outcome

$\beta$0 = 40.4489 , $\beta$ 1 = 0.4578

Second test grade(Yi) = 40.4489+ (0.4578) First test grade(Xi)