Question

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data42.datgives the scores of 60 students who did this. How can we relate the two tests?

(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations.

(b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)

ACT =	+ (SAT)
t =
P =

(c) What is the correlation between the two tests? (Round your answer to three decimal places.)

Data set

obs     sat     act
1       708     15
2       1064    26
3       912     25
4       953     23
5       1251    28
6       648     12
7       1005    21
8       664     16
9       604     17
10      945     25
11      1034    21
12      895     16
13      935     19
14      909     24
15      938     17
16      777     21
17      703     14
18      1242    25
19      971     21
20      817     17
21      885     18
22      1138    23
23      909     17
24      788     21
25      1064    19
26      1170    26
27      806     15
28      923     20
29      1170    21
30      579     16
31      888     22
32      1207    24
33      871     22
34      1117    25
35      1070    17
36      767     17
37      969     22
38      1027    30
39      931     23
40      933     21
41      965     26
42      960     22
43      787     17
44      1002    20
45      1221    33
46      1042    24
47      897     22
48      1061    24
49      898     18
50      720     11
51      976     18
52      1066    25
53      931     18
54      593     12
55      735     16
56      544     10
57      871     17
58      875     21
59      921     22
60      559     15

Answer 1

Date: 05/06/2019 Answer a and b) The scatterplot ofACT (y) on SAT (x) is, By using MINITAB software, draw the scatterplot with the help of following steps: 1) 2) 3) 4) 5) Import the given data into worksheet Select Scatterplot from the Graph Choose With Regression graph options and click Ok Select the X variables and Y variables Click Ok

Scatterplot of ACT vs SAT 35- 30- 25 20- 15- 10- 500 600 700 800 900 1000 1100 1200 1300 SAT From the MINITAB output, the scatterplot of ACT (y) increasing pattem in scatterplot due to as SAT score increases as ACT score increases and there is no unusual data as well as data does not appear to contain any outlier. Most of the data are fall nearly straight line on SAT (x) conclude there is АСТ

The lest-squares regression equation is By using Excel software, find regression equation with help of following steps: 1) 2) 3) 4) 5) Import the data Select Data Analysis from Data menu Select Regression and click Ok. Input Y Range and Input X range Click Ok SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.59603043 Standard Error Observations 0.77645178 0.60287737 2.93741417 60 Coefficients Standard Error P-value t Stat Intercept SAT 1.3546971 2.045572858 0.662258 0.510429 0.002200414 9.383528 3.11E-13| 0.02064765

From the Excel output, the regression equation is =1.355 +0.021 x The regression slop is 0.021 and intercept is 1.355 The t-test statistics is From Excel output, the t-test statistics is 9.38 The p-value is From Excel output, thep-value is |0.0000 c) The correlation coefficient is r=v V0.6029 (From Excel output) 0.776

The correlation coefficient is |0.776