Question

A study of child development finds a positive and linear relationship between the height (in inches) and weight (in pounds) of a sample of first-grade students. If we use the data from this study to construct a regression equation, with age as the explanatory variable and ability test score as the response variable, we know for certain that We need more information to be able to answer this question. the intercept will be positive. the slope and intercept will both be positive. slope will be positive. Province

Answer 1

Since there is a positive and linear relationship between the height (in inches) and weight (in pounds),

so if we construct a regression equation with age as the explanatory variable and ability test score as the response variable, we know for certain that -

• The slope will be positive.

Formula for slope : $b_1 = r*\frac{s_y}{s_x}$ , since r > 0, and s_x > 0 and s_y > 0, that implies b₁ > 0.

Formula for intercept : $b_0 = \bar{y}-b_1*\bar{x}$ , if $\bar{y}<b_1*\bar{x}$ , then intercept b₀ can be negative.