o becawse there are oukers ana thay do not appeas te forw 4. (16 Pts) Applicants

Question

o becawse there are oukers ana thay do not appeas te forw 4. (16 Pts) Applicants for a particular job, which involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. Data were obtained in a study of the relationship between the number of years applicants have studied Spanish (x, Years studied) and their score on the test (y: Test Score). Answer the following questions using the information from StatCrunch output shown on the next page. It is known that a linear regression model is appropriate for the data. a) Which variable is the independent or predictor variable and which is the dependent or response variable? indepanden y-ependent b) Determine the regression equation. c) What % of the variation in y is explained by the regression equation? What % is unexplained What is the predicted test score for 4 years of studying Spanish? Is this interpolation or extrapolation.? d) Page 5 of 6

Explanation / Answer

Question 4:

a) Here we are already given in the output first few lines that Score is the dependent variable and Years is the independent variable.

b) From the table of parameter estimates, the regression equation obtained here is given as:

Score = 31.533333 + 10.904762*Years

c) Here we are given that value of R2 as 0.83012784

This is called the coefficient of determination which means that 83.012784% of the variation in the dependent variables here is explained by the independent variable and therefore 100 - 83.012784% = 16.987216% of the variation is unexplained.

d) From the given output we see that predicted Y value for X = 4 as 75.15238

Here we are not given the raw data. In case the value of X = 4 lies in the given data from which the regression model is built, then this is a case of interpolation, otherwise this is a case of extrapolation.

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