For the data given Fit a least squares line to the data Plo

For the data given :

-Fit a least squares line to the data.

-Plot the data and graph the line.

-Calculate r and r²; interpret their values.

-Is the model useful (90% confidence interval) for predicting y?

-Estimate y given x = 10. Use a 90% confidence interval

Y	X
58.91917314	17.9441336
13.57450242	6.12632559
29.3510094	12.8002848
45.64305354	15.57287621
-2.648422623	8.695513665
44.06502304	12.80388374
50.20597577	14.24341375
30.07622849	5.649884292
37.53191814	12.02881596
39.98763409	13.4763698
46.96164978	19.19645139
25.60818927	9.168443517
42.66781837	13.52147073
33.77291567	6.092608631
39.12879011	11.56356009
43.07872857	14.30645052
43.51514269	9.524191495
19.97826821	1.344326967
44.85200986	18.00158661
36.10558182	9.339117519
8.74116488	5.553085772
62.22326432	11.92228699
19.10002051	4.344504869
4.429185513	6.03277689
33.18251152	4.634981732
37.69023567	17.93512977
32.82332528	7.377868327
47.79558313	15.74506664
31.4553294	1.182070999
33.75199949	12.46278751
21.86032694	8.275259269
57.83697505	13.76913395
20.31702021	8.661682752
26.10576109	5.95641473
26.73859946	0.082539129
11.46490278	12.56121459
30.5172699	19.83131481
42.65479476	14.86181506
58.11222346	16.9411625
78.01812341	12.94288059
51.01794935	18.95044451
13.87470654	14.55600802
54.42381195	19.23347452
13.21304338	6.226046222
18.18269123	2.14775948
5.081059876	2.040475183
29.01467642	11.42179127
13.78004308	1.962144154
4.037299486	0.557280575
36.08791397	17.42440261
10.82561657	1.535862587
60.75949037	11.86784676
19.2654877	13.26464288
30.71052795	5.894218568
18.28906623	1.723702036
44.0640593	15.24302873
49.28771824	16.84514569
71.7365424	17.6801154
1.591984571	0.024247438
41.25121241	16.64329523
17.70185656	0.979867578
38.63051186	0.762031575
-1.361124256	6.065775263
58.30213707	17.60707338
10.29320205	9.370296876
-12.80911099	0.589688381
63.99814441	15.14417208
39.89835626	11.26539367
29.46070879	9.772175717
26.74835913	6.872940569
12.07361556	11.06240389
25.6395985	7.992690392
21.14998145	4.61432529
20.7040192	1.259273205
36.98005302	14.00887369
0.718428855	3.864104412
28.07984886	12.78772697
30.17861878	9.251116269
90.30933506	18.68362385
-4.52484206	7.165764446
12.941613	3.248634124
42.11788439	8.150724049
51.59458	12.59120492
51.60946033	19.49341114
65.88231016	15.84169803
30.71155647	3.616634255
46.09816083	18.45406965
32.2485384	1.652796065
56.53126019	7.239351102
43.37319811	17.10232366
13.82991967	8.621716957
20.58527511	5.292266003
56.462476	14.62785029
36.2813413	15.16897518
14.05597424	3.870469984
29.26498968	12.70525191
41.37653997	9.339120222
23.19082164	7.864050797
8.636308408	1.909121706
23.70099472	8.285990079
23.97055423	11.4312186

The equation of the line best fit is given as:

Y = 2.2755 X + 9.5767

R = 0.67772

R² = 0.4593

The values of R and R² are pretty low. So, the model is not very accurate in predicting. the R² determines the amount of regression explained by this line.

For X = 10, we have the predicted value of Y as:

Y-hat = (2.2755 * 10) + 9.5769

= 32.331

Hope this helps. Refer to the table for p-values and other statistics

58.91917314

17.94413360

SUMMARY OUTPUT

13.57450242

6.12632559

29.35100940

12.80028480

Regression Statistics

45.64305354

15.57287621

Multiple R

0.677728855

-2.64842262

8.69551367

R Square

0.459316402

44.06502304

12.80388374

Adjusted R Square

0.453854951

50.20597577

14.24341375

Standard Error

14.20313791

30.07622849

5.64988429

Observations

101

37.53191814

12.02881596

39.98763409

13.47636980

ANOVA

46.96164978

19.19645139

Significance F

25.60818927

9.16844352

Regression

16965.73

84.10154

7.04E-15

42.66781837

13.52147073

Residual

19971.18

201.7291

33.77291567

6.09260863

Total

100

36936.91

39.12879011

11.56356009

43.07872857

14.30645052

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 90.0%

Upper 90.0%

43.51514269

9.52419150

Intercept

9.57669929

2.841302

3.370533

0.001071

3.938941

15.21446

4.859027

14.29437

19.97826821

1.34432697

2.275473326

0.248125

9.170689

7.04E-15

1.78314

2.767806

1.863489

2.687457

44.85200986

18.00158661

36.10558182

9.33911752

8.74116488

5.55308577

62.22326432

11.92228699

19.10002051

4.34450487

4.42918551

6.03277689

33.18251152

4.63498173

37.69023567

17.93512977

32.82332528

7.37786833

47.79558313

15.74506664

31.45532940

1.18207100

33.75199949

12.46278751

21.86032694

8.27525927

57.83697505

13.76913395

20.31702021

8.66168275

26.10576109

5.95641473

26.73859946

0.08253913

11.46490278

12.56121459

30.51726990

19.83131481

42.65479476

14.86181506

58.11222346

16.94116250

78.01812341

12.94288059

51.01794935

18.95044451

13.87470654

14.55600802

54.42381195

19.23347452

13.21304338

6.22604622

18.18269123

2.14775948

5.08105988

2.04047518

29.01467642

11.42179127

13.78004308

1.96214415

4.03729949

0.55728058

36.08791397

17.42440261

10.82561657

1.53586259

60.75949037

11.86784676

19.26548770

13.26464288

30.71052795

5.89421857

18.28906623

1.72370204

44.06405930

15.24302873

49.28771824

16.84514569

71.73654240

17.68011540

1.59198457

0.02424744

41.25121241

16.64329523

17.70185656

0.97986758

38.63051186

0.76203158

-1.36112426

6.06577526

58.30213707

17.60707338

10.29320205

9.37029688

-12.80911099

0.58968838

63.99814441

15.14417208

39.89835626

11.26539367

29.46070879

9.77217572

26.74835913

6.87294057

12.07361556

11.06240389

25.63959850

7.99269039

21.14998145

4.61432529

20.70401920

1.25927321

36.98005302

14.00887369

0.71842886

3.86410441

28.07984886

12.78772697

30.17861878

9.25111627

90.30933506

18.68362385

-4.52484206

7.16576445

12.94161300

3.24863412

42.11788439

8.15072405

51.59458000

12.59120492

51.60946033

19.49341114

65.88231016

15.84169803

30.71155647

3.61663426

46.09816083

18.45406965

32.24853840

1.65279607

56.53126019

7.23935110

43.37319811

17.10232366

13.82991967

8.62171696

20.58527511

5.29226600

56.46247600

14.62785029

36.28134130

15.16897518

14.05597424

3.87046998

29.26498968

12.70525191

41.37653997

9.33912022

23.19082164

7.86405080

8.63630841

1.90912171

23.70099472

8.28599008

23.97055423

11.43121860

For the data given : -Fit a least squares line to the data. -Plot the data and graph the line. -Calculate r and r2; interpret their values. -Is the model useful

For the data given Fit a least squares line to the data Plo

Solution

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