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The following is a sample of the grades for 10 high school students who took bot

ID: 3262715 • Letter: T

Question

The following is a sample of the grades for 10 high school students who took both Physics and Algebra. Test to see if a relationship exists. Show the best fit line: Y = B1X + B0 (use actual values from the problem). How strong is the relationship? If I get an 86 on my Algebra test what would you predict that my Physics grade will be?

Student           Algebra           Physics

1                      75                    82

2                      80                    78

3                      93                    86

4                      65                    72

5                      87                    91

6                      71                    80

7                      98                    95

8                      68                    72

9                      84                    89

10                    77                    74

Algebra is the independent variable.

Explanation / Answer

Run Regression in Excel

there exits a relationship

since corrrrelation coefficient=0.872098

there exist a strong positive relationship between algebra and physics.

From Anova tests

F=25.41 and p=0.001

since

p<0.05

Reject Null hypothesis

Therefore model is significant.

There is sufficient evidence that relationship exists between algebra and physics.

Regression equation is

physics=0.661(Algebra)+29.129

slope=0.661

y intercept=29.129

If I get an 86 on my Algebra means put x=86

physics=0.661(86)+29.129

=85.975

=86

physics=86

we would you predict that Physics grade will be 86.

SUMMARY OUTPUT Regression Statistics Multiple R 0.872098 R Square 0.760556 Adjusted R Square 0.730625 Standard Error 4.23384 Observations 10 ANOVA df SS MS F Significance F Regression 1 455.4968 455.4968 25.41068 0.001001 Residual 8 143.4032 17.9254 Total 9 598.9 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 29.12903 10.55383 2.760045 0.024673 4.791865 53.4662 Algebra(x) 0.66129 0.131185 5.040901 0.001001 0.358777 0.963803