The graph shows an increasing trend and that there is a positive association between the size of the diamond (carat) and the cost (in US dollars). It means that as the size of the diamond (carat) increases, the cost of the diamond shall also increase.
- Linear Model:
The linear model given above can help us predict the cost of the diamond.
- To check if the linear model is appropriate, it needs to fulfill three conditions these include, linearity, nearly normal residuals and constant variability and the data set given in this question fulfills these conditions.
- The slope of this model is 8225.1. it helps to estimate the average change in the dependent variable (cost) for each unit change in the independent variable (size).
- The Intercept of this model is -558.52, it helps to measure the variability in the response when the independent variable is equal to zero.
- As Coefficient of Determination that is r^2 = .9875, after taking square root we shall get the value of r=.99373. The value of correlation coefficient r is closer to 1, it means that there is a strong positive correlation between the two variables.
- Cost of a quarter of diamond and the residual values are given below:
- Firstly the dependent variable (the size of diamond) each value was divided by four to get the required column. The linear equation was calculated again. After putting the values of column Quarter of diamond in the regression equation and solving it we obtained the Y1^. Finally, by subtracting the observed value (Y) from the estimating value (Y1^) we get the value of residual error.
|Cost of Diamonds ($)||Size of Diamonds||y^||Residual (Y-Y^)||A quarter of diamond (x1)||Revised Cost Y1^||Residual (y-y^)|