Question

Disk drives have been getting larger. Their capacity is now often given in terabytes​(TB) where 1 TBequals=1000 ​gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown to the right. Find and interpret value of Rsquared2.

Capacity​ (in TB) Price​ (in $) 0.0800.080 34.4534.45 0.1000.100 36.9936.99 0.2700.270 38.5538.55 0.3400.340 53.9553.95 2.02.0 223.00223.00 3.03.0 292.79292.79 4.04.0 424.79424.79

What is the value of

Upper R squaredR2​?

nothing​%

​(Round to two decimal places as​ needed.)What is the interpretation of

Upper R squaredR2​?

The value of

Upper R squaredR2equals=nothing​%

indicates the percentage of the variability in the

▼

price

capacity

of these disk drives that

▼

can

cannot

be explained by the variability in the

▼

price

capacity

of the drives.

​(Round to two decimal places a

Answer 1

Capacity​ (in TB) X	Price​ (in $) Y
0.08	34.45
0.1	36.99
0.27	38.55
0.34	53.95
2	223
3	292.79
4	424.79

Correlation Coefficient ( r ) = N x ∑ XY - ( ∑ X ) ( ∑ Y ) / √ N x ( ∑ X2 - ( ∑ X )2 √ N x ( ∑ Y2 - ( ∑ Y )2              

Coefficient of Determination ( r squared ) = r x r.

              

Adjusted/ Upper r squared = 1- [(1-r^2)(n-1)/ (n-k-1)]      

where-

N is the number of points in your data sample. In this case- 7      

K is the number of independent regressors, i.e. the number of variables in your model, excluding the constant. In this case-1     

              

R^2 (R squared)=             0.994517522

Upper R^2 (R squared)=               0.993421027

              

1-R^2= 0.005482478

1- Upper R^2=   0.006578973

              

A high value of R2 implies that the dependent variable Y (Price) is explained by the independent variable (Capacity) to a large extend; 99.34% to be exact. There is still some amount of variability in the dependent variable that is not explained by the independent variable to the extent (1- R^2=) 0.66%. Upper R^2 assumes all the variable included in the regression contribute to the value of dependent variable. In this case, since there is only one independent variable (capacity), the value of R^2 and upper R^2 are not very different. The difference in values is partially due to smaller number of observations.