Why must the R-Squared value of a regression be less than 1?

Answer 1

#SSReg le SST#

Note that #R^2= ("SSReg")/(SST)# where SST= SSReg +SSE and we know that sum of squares are always #ge 0#.
So #SSE ge 0# #implies SSReg +SSE ge SSReg# #implies SST ge SSReg# #implies (SSReg)/(SST) le 1# #implies R^2 le 1#
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Answer 2

The R-squared value of a regression must be less than 1 because it represents the proportion of the variance in the dependent variable that is predictable from the independent variables. It is a measure of how well the independent variables explain the variability of the dependent variable. Since R-squared is a proportion, its value ranges from 0 to 1, where 0 indicates that the independent variables do not explain any of the variability of the dependent variable, and 1 indicates that the independent variables perfectly explain all of the variability of the dependent variable. Therefore, an R-squared value greater than 1 would imply that the model is explaining more variability than actually exists in the data, which is not possible. Thus, the R-squared value is constrained to be less than or equal to 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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