Question

How old are you in whole years?	What is your major?	What is your current GPA?
17	Business Administration	3.7
20	Business Administration	2.5
21	Communications	3.1
21	Social Sciences	2.5
19	Social Sciences	3
19	Nursing	4
27	Communications	3.26
21	Communications	3.5
31	Business Administration	3.4
19	Education	3
37	Business Administration	3
34	Education	4
20	Business Administration	3.65
27	Nursing	1.98
36	Education	4
45	Nursing	3
38	Nursing	3.85
19	Education	3.6
20	Nursing	1.97
24	Business Administration	4

  What are the TWO variables?

Is the variable, age, in years, qualitative or quantitative?

Is the variable, age, discrete, continuous, or neither?

What is the level of measurement (nominal, ordinal, interval, ratio) for the variable, age?

Is the variable, GPA, qualitative or quantitative?

Is the variable, GPA, discrete, continuous, or neither?

What is the level of measurement (nominal, ordinal, interval, ratio) for the variable, GPA?

What is the y-intercept?

What is the slope?

What is the R-value?

What does the R-value indicate about this correlation?

What is the r-squared value?

What does the R-value indicate about this correlation?

What is the hypotheses to test for significance of the linear model?

What is the p-value?

What is my conclusion at the 0.05 level of significance?

Can I make predictions on the model? Why?
Using the regression equation, predict the Grade Point Average for a traditional student who is age 20, if you can make predictions

Is there a relationship between a student’s age(x), in years, and their Grade Point Average (GPA) (y)? Please answer in a complete sentence.

Answer 1

1)There are actually three variables in the data. Age and current GPA are quantitative and Major is a qualitative variable.

2) Age in years is a discrete variable as it cannot take any value between two consecutive values, say between 17 and 18.

3) age is an interval variable. Takes values in an interval of one year

4)GPA is quantitative , continuous and ratio type variable as it takes any value between an interval. Generally scores like IQ are ratio type variable.

5) We perform a linear regression analysis for the variables GPA( dependent ) and Age in years( independent) and the results are given below

The R value is the square root of R^2 value in the above table.

Therefore the R value is 0.16

R value indicates that the correlation between the variables is very poor or low positive correlation

The hypothesis test to test for the significance of linear model is

The test statistic to test the above hypothesis is

The p value is the value obtained from the t table for 18 degrees of freedom and 5% significance level ie 0.2508. Since pvalue is >0.05 we fail to reject the null hypothesis. that population correlation coefficient =0. So predictions based on the model cannot be relied as there is no relationship between the variables.R-square value (0.025 ) indicates that only 2.5% of the variation in dependent variable (GPA) can be explained by the Age in years

The relationship between Age and GPA is not statistically significant at 5% significance level. So there is no relationship between them.