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The 95% Confidence Interval for the Predicted Effect of a General

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The 95% confidence interval for the predicted effect of a general change in X is a. (β1Δx1.96SE(β1)×Δx,β1Δx+1.96SE(β1)×Δx)\quad \left( \beta _ { 1 } \Delta x - 1.96 \operatorname { SE } \left( \beta _ { 1 } \right) \times \Delta x , \beta _ { 1 } \Delta x + 1.96 \operatorname { SE } \left( \beta _ { 1 } \right) \times \Delta x \right)
b. (β^1Δx1.645SE(β^1)×Δx,β^1Δx+1.645SE(β^1)×Δx)\left( \widehat { \beta } _ { 1 } \Delta x - 1.645 \operatorname { SE } \left( \hat { \beta } _ { 1 } \right) \times \Delta x , \widehat { \beta } _ { 1 } \Delta x + 1.645 \operatorname { SE } \left( \hat { \beta } _ { 1 } \right) \times \Delta x \right)
c. (β^1Δx1.96SE(β^1)×Δx,β^1Δx+1.96SE(β^1)×Δx)\left( \hat { \beta } _ { 1 } \Delta x - 1.96 \operatorname { SE } \left( \hat { \beta } _ { 1 } \right) \times \Delta x , \widehat { \beta } _ { 1 } \Delta x + 1.96 \operatorname { SE } \left( \hat { \beta } _ { 1 } \right) \times \Delta x \right)
d. (β^1Δx1.96,β^1Δx+1.96)\left( \widehat { \beta } _ { 1 } \Delta x - 1.96 , \widehat { \beta } _ { 1 } \Delta x + 1.96 \right)

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Definitions:

Two-Tailed

In hypothesis testing, it refers to the methodology that considers both directions of a possible effect, allowing for investigation of deviations in two opposite directions from the null hypothesis.

Pearson Correlation

A metric that quantifies the linear relationship between two variables, providing a value in the range of -1 to 1.

Negative Number

A number less than zero, typically represented with a minus sign in front, indicating a value opposite to its positive counterpart.

Null Hypothesis

A hypothesis that there is no significant difference or effect, typically used as a starting assumption in hypothesis testing.

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