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Answer 1
Part a)
| S.no | X | Y | X-Mean | Y-mean | (X-mean) *(Y-mean) |
| 1 | 420 | 2.8 | -105 | -0.4 | 42 |
| 2 | 610 | 3.6 | 85 | 0.4 | 34 |
| 3 | 625 | 3.75 | 100 | 0.55 | 55 |
| 4 | 500 | 3 | -25 | -0.2 | 5 |
| 5 | 400 | 2.5 | -125 | -0.7 | 87.5 |
| 6 | 450 | 2.7 | -75 | -0.5 | 37.5 |
| 7 | 550 | 3.5 | 25 | 0.3 | 7.5 |
| 8 | 650 | 3.9 | 125 | 0.7 | 87.5 |
| 9 | 480 | 2.95 | -45 | -0.25 | 11.25 |
| 10 | 565 | 3.3 | 40 | 0.1 | 4 |
| Sum | 5250 | 32 | 371.25 | ||
| Mean | 525 | 3.2 | |||
| Covariance | 41.25 | ||||
| Correlation | 0.978839596 |
Part b) The coefficient of correlation indicates that X and Y values have a high positive correlation. This means that 2 variables move on the same direction. If X increases, Y also increases.
The coefficient of covariance is positive which tells us that the two variable X and Y tend to increase or decrease together (move in the same direction)
Part c) Using the formulas for b1 = SSxy/SSx and b0 = Y-bar - b1(x-bar), I calculated the values and put them into equation.
Equation is: 0.415625 + 0.005304*X
Answer 2
Part a) The regression output shows a t reg value of -0.528. Whereas the critical value of 2-tailed test takes the value -1.96 which is less than -0.528. Hence, H0 is accepted in the favour of alternative hypothesis. No, the coefficient of price is not significantly different from zero.
Part b) R2, the coefficient of determination has the value 0.01104 which means that the model only explains 1.1% of the variability around its mean.
Part c) No, since the hypothesis test fails, it means that the coefficient of price is insignificant. R2 is also low which means that there are many unobserved factors that affect sound quality. Moreover, even if the hypothesis testing were successful, the coefficient has a negative sign which means that a higher price means low sound quality.
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