Question

Data on average high temperatures​ (in degrees​ Fahrenheit) in July and precipitation​ (in inches) in July for 48 cities is used to find a regression line and correlation coefficient. PRECIP​ = 2.0481​ + 0.0067 HIGH R​ (correlation coefficient)​ = 0.0358 ​(1) Give the value of the slope of the regression line. ​(2) Identify the predictor variable in this context. ​(3) Identify the response variable in this context. ​(4) Clearly interpret the numerical value of the slope in the context of the​ problem, namely connecting​ "precipitation" and​ "average high​ temperature". ​(5) Predict the amount of precipitation​ (two places past the​ decimal) for a city that has an average high temperature in July of 87.31 degrees Fahrenheit.

Answer 1

Explained below.

Explanation:

The regression equation to predict amount of precipitation​ (in inches) in July from the average high temperatures​ (in degrees​ Fahrenheit) in July is as follows:

PRECIP​ = 2.0481​ + 0.0067 HIGH

(1)

The value of the slope of the regression line is, 0.0067.

(2)

The predictor variable in this context is the average high temperatures​ (in degrees​ Fahrenheit) in July.

(3)

The response variable in this context is the amount of precipitation​ (in inches) in July.

(4)

The slope of a regression line is average rate of change in the dependent variable with one unit change in the independent variable.

The slope here is 0.0067.

This value implies that the average rate of change in the amount of precipitation​ (in inches) in July increases by 0.0067 inches with every 1°F increase in the average high temperatures​.

(5)

Compute the mount of precipitation for a city that has an average high temperature in July of 87.31°F as follows:

PRECIP​ = 2.0481​ + 0.0067 HIGH

= 2.0481​ + 0.0067 × 87.31°F

= 2.633077

≈ 2.63 inches.