A fan of television game shows has observed that, in general, the more educated

Question

A fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief she gathers data about the last ve winners of her favorite game show. She records their winnings in dollars and the number of years of education. The data are as follows. She estimated a regression model using winnings as the dependent variable (Y) and years of education as the independent variable (X) She used the ordinary least squares estimator What is the predicted change in winnings when the education of the winner increases by a year? decrease by $37.5 decrease by $25 decrease by $75 decrease by $50 decrease by $62.5

Explanation / Answer

Solution:-

Formula used,
Y = a + bX
where,
b = r (SDy/SDx)
a = Ybar - bXbar

Where,

Y = Least Square Regression Line Equation
b = The slope of the regression line
a = The intercept point of the regression line and the y axis.  
X = Mean of x values
Y = Mean of y values
SDx = Standard Deviation of x
SDy = Standard Deviation of y

Using excel sheet inorder to calculate Y, we get

Least Square Regression Line Equation Y = -25x + 850

As we can see that slope, a = -25

Therefore, the perdicted change in winning when the education of the winner increases by a year decrease by $25.

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