6 110 points s0s (a) The picture above shows four different scattms wh o te cs w

Question

6 110 points s0s (a) The picture above shows four different scattms wh o te cs wo ag oprute to use linear regression toappronantethe falnemhphenween % sndy? hody briefly (b) Think about airline tickets. If you carried out a linear regression with the distance waveled by the flight as the independent variable and price of the ticket as the dependent vaie, would you expect the coefficient of the independent variable in the segressios eation so positive, negative or zero? Justify briefly (c) Think about used car sales. If you carried out a linear segression witds sale price of the car as the dependent variable and age of the car in years as the independent varialble, wold you expect the coefficient of the independent variable in the regression to be youitove, negatiove or zero? Justify briefly (d) In (c) above, would you expect a very high R-squared value, such as 0.90, or something more modest such as 0.607 Justify briefly

Explanation / Answer

a) In case A, the data has linear trend with positive correlation, i.e slope of line is positive. So we use linear regression for this case.

In case C, the variables x and y has strong linear association with negative slope, i.e having negative correlation. So we use linear regression for this case.

For the other two cases, the data does not show linear trend, so it would not be appropriate use linear regression for these cases.

b) For the case of Airline ticket, If distance travelled is independent variable and price of ticket is dependent variable, then both are positively correlated, i.e price of ticket increases with increasing distance of flight. So the coefficient of independent variable in regression equation will be positive.

c) For the the case of used car sales, If the age of car is independent variable and sale price of car is dependent variable, then both are negatively correlated, i.e sale price of car will decrease as the age of car increases. So the coefficient of independent variable in regression equation will be negative.

d) In case c), since the independent variable has highly significant effect on dependent variable and has strong negative linear relationship. Therefore we expect a very high R-squared value such as 0.90 or more.

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