Question

Is there a relation between the age difference between​ husband/wives and the percent of a country that is​ literate? Researchers found the​ least-squares regression between age difference​ (husband age minus wife​ age), y, and literacy rate​ (percent of the population that is​ literate), x, is y=−0.0437x+7.5. The model applied for 17≤x≤100. Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. For every unit increase in ______ the _____ falls by ______ ​units, on average.

Answer 1

Answer:

$y = \beta_1 x + \beta_o$

With $\beta_1$ representing the slope we have that:

$\hat \beta_1 = -0.0437$

$\hat \beta_o = 7.5$

And we are interest on this case the interpretation about the slope and we can conclude that:

For every unit increase in literacy rate (percent of the population that is literate) the age difference (husband minus wife age) ​falls by 0.0437 units, on average.

Step-by-step explanation:

For this case we have that the regression model adjusted between age difference (husband minus wife age) representing the y variable and literacy rate (percent of the population that is literate) representing the variable x is given by:

$y= -0.0437 x + 7.5$ where $17 \leq x\leq 100$

And we know that the method used in order to adjust the regression line was least squares.

For this case our dependent variable is y = age difference (husband minus wife age) and the independent variable is x=literacy rate (percent of the population that is literate)

If we compare the regression model adjusted with the linear regression model:

$y = \beta_1 x + \beta_o$

With $\beta_1$ representing the slope we have that:

$\hat \beta_1 = -0.0437$

$\hat \beta_o = 7.5$

And we are interest on this case the interpretation about the slope and we can conclude that:

For every unit increase in literacy rate (percent of the population that is literate) the age difference (husband minus wife age) ​falls by 0.0437 units, on average.