Question

1) A student wishes to determine the association between Hours Studied and Test Score. She also wants to determine the association between Hours of Sleep before the Test and the Test Score.

Hours Studied	1	3	2.5	4	5	5	3	4
Hours Slept	6	7	7	8	8	8	5	6.5
Test Score	72	80	78	90	94	96	88	84

1. Which factor (hours studied or hours slept) is a stronger association with test score? (Show data to support this).

Hours Slept is a stronger association

2. What is the r-squared for hours studies vs test score and interpret it.

3. What is the regression equation for each association above and use the Linreg T test to determine whether the equations are valid predictors of Test Score.

1. Study vs Test score:
2. Sleep vs Test score

4. If someone studied 3.5 hours, what would be the predicted test score?                                         Is using your equation a valid way to predict this?

Answer 1

The regression output for Test score vs Hours studied is as follows

The regression output for Test score vs Hours slept is as follows

Question (1)

The Multiple R value gives us how strong the relationship is between Independent and Dependent variables

The Multiple R value in Hours studied vs Test score is 0.92997 which is more than the The Multiple R value in Hours slept vs Test score of 0.5197

So Hours studied has a stronger association with test score

Question (2)

R-square value for  hours studies vs test score from the above image is 0.864847 or 86.4847%

R-square value gives us how much of variation in dependent variable is explained by the independent variable or R-square value gives us how well the regression model fits the data. Higher the R-square value, the better is the fit

Here R-square value is 0.864847 which means 86.4847% of the variation in Test score is explained by Hours Studied. R-square value of 0.864847 represents a good fit of the model for the data

Question (3)

The regression equation for Test score vs Hours studied is

Predicted Test Score = 65.6216 + 5.7101 * Hours Studied

The regression equation for Test score vs Hours slept is

Predicted Test Score = 57.711 + 3.9696 * Hours Slept

If the Significant F score is less than 0.05, then we can say that the independent variable is a good predictor of dependent variable

Here Significant F score for Test score vs Hours studied is 0.000814 which is less than 0.05, hence hours study is a good predictor of Test score

Here Significant F score for Test score vs Hours slept is 0.1868 which is more than 0,05, hence hours slept is not a good predictor of Test score

Question (4)

The regression equation for Test score vs Hours studied is

Predicted Test Score = 65.6216 + 5.7101 * Hours Studied

Here Hours Studied = 3.5

So Predicted Test Score = 65.6216 + 5.7101 * 3.5

= 85.60695

Yes our equation is vaild since the ignificant F score for Test score vs Hours studied is 0.000814 which is less than 0.05 and hours study is a good predictor of Test score