Question

Getting in to a prestigious law school can have lasting effect’s on lawyer’s careers, thus the admission process is important. One measure that admissions officers look at is prospective law student’s LSAT scores. Because of that, companies that specialize in preparing students for the LSAT have sprouted up. Altair Test Preparation, in an effort to differentiate themselves from the rest and to assure their clients that they are being provided with what really is having an effect, have decided to conduct some research to identify what has the greatest impact on student’s LSAT scores. All companies advertise that the number of hours they give them study sessions is what makes a difference. Based on the results, Altair will either recommend the hours needed to obtain a “good” score vs an “excellent” score. (Good is 155, excellent is 169), or will decide to investigate other learning interventions, and academic counseling which might have a greater impact.

Altair collected a sample of 50 students, who in the previous year, were their clients and subsequently took the LSAT. The looked at the relationship between the number of hours they used the service, and their LSAT score. You, as the statistician, will run the analysis and make your recommendations to Altair Test Preparation.

Your report should have the following qualities:

• What LSAT score would you predict for a student that used the service for 10 hours? What

  recommendation would you give the student concerning the number of hours they have used

  the service?

• Your final conclusion should use both the 95% confidence and prediction intervals. Improper use

  of these and corresponding wrong/sloppy interpretations is highly penalized.

• Use Data Analysis for Regression and the Regression Template provided on the course website

  for the intervals.

• data below:

  • Hours	LSAT
    13	161
    13	158
    11	147
    14	164
    3	124
    10	130
    4	114
    7	131
    12	156
    7	135
    8	150
    11	150
    9	121
    10	160
    18	170
    17	155
    13	160
    14	154
    5	132
    11	156
    10	153
    8	150
    15	172
    7	141
    9	140
    11	155
    10	149
    8	149
    5	140
    6	142
    14	167
    12	166
    10	161
    14	162
    12	154
    12	156
    8	167
    12	160
    10	156
    11	170
    15	177
    5	130
    8	151
    11	160
    15	171
    11	154
    6	143
    6	165
    13	165
    9	145

Answer 1

Solution:

Here, we have to use regression analysis for the prediction of the dependent variable LSAT score and the independent variable number of hours the service used. The regression model by using excel is given as below:

Regression Statistics
Multiple R	0.737671352
R Square	0.544159023
Adjusted R Square	0.534662336
Standard Error	9.643695665
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5328.938428	5328.938428	57.2998796	0.00
Residual	48	4464.041572	93.00086607
Total	49	9792.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	120.5983989	4.364272582	27.63310418	3.95804E-31	111.8234409	129.3733569
Hours	3.058635582	0.404064673	7.569668394	9.90171E-10	2.246209121	3.871062042

From above regression output, it is observed that the correlation coefficient between the two variables is given as 0.7377, which means there is a considerable high positive linear relationship exists between the given two variables. The value of the R square or the coefficient of determination is given as 0.5442, which means about 54.42% of the variation in the dependent variable LSAT score is explained by the independent variable number of hours the service used.

The P-value for this regression model is given as 0.00 approximately. So, we reject the null hypothesis. There is sufficient evidence to conclude that the given regression model is statistically significant. The intercept and coefficient of independent variable are statistically significant as their corresponding P-values are approximately equal to 0.00.

The required regression equation is given as below:

LSAT = 120.5984 + 3.0586*Hours

Y = 120.5984 + 3.0586*X

Now, we have to predict the value for LSAT for hours = 10

LSAT = 120.5984 + 3.0586*10

Predicted LSAT = 151.1844

For the above regression model, the slope is positive, that is, correlation is positive, this means it is recommended to use more hours of service to increase LSAT score. As number of service hours increases, the LSAT score increases.