Husbands and wives, Part II

Husbands and wives, Part II#

The scatter plot below summarizes husbands’ and wives’ heights in a random sample of \({{ params.sample}}\) married couples in Britain, where both partners’ ages are below \(65\) years. The summary output of the least squares fit for predicting a wife’s height from the husband’s height is also provided in the table.

Part 1#

Select the hypotheses.

Answer Section#

  • \(H_0: \beta_1 = 0; H_A: \beta_1 \ne 0\)

  • \(H_0: \beta_1 = 0; H_A: \beta_1 > 0\)

  • \(H_0: \beta_1 < 0; H_A: \beta_1 > 0\)

Part 2#

Is there strong evidence that taller men marry taller women?

Answer Section#

  • The data provide convincing evidence that wives’ and husbands’ heights are positively correlated. The p-value, as reported in the table, is smaller than 0.05, so we reject \(H_0\).

  • The data does not provide convincing evidence that wives’ and husbands’ heights are positively correlated. The p-value, as reported in the table, is significant, so we fail to reject \(H_0\).

  • There is no sufficient information to make a conclusion.

Part 3#

What slope value is multiplied by the wife’s height when predicting the wife’s height from the husband’s height?

hint: Write the equation of the regression line first.

Answer Section#

Part 4#

What intercept value is used when predicting a wife’s height from a husband’s height?

hint: Write the equation of the regression line first.

Answer Section#

Part 5#

Interpret the slope and intercept in the context of the application and select the correct options.

Answer Section#

  • Slope: For each additional inch in husband’s height, the average wife’s height is expected to be an additional (slope value) inches on average.

  • Slope: For each additional inch in wife’s height, the average husbands’s height is expected to be an additional (slope value) inches on average.

  • Intercept: Men who are 0 inches tall are expected to have wives who are on average, (intercept value) inches tall.

  • Intercept: Men who are (intercept value) inches tall are expected to have wives who are on average, 0 inches tall.

  • The intercept here is meaningless, and it serves only to adjust the height of the line.

Part 6#

Given that \(R^2 = {{params.correlation}}\), what is the correlation of heights in this data set?

Answer Section#

Please enter a numeric value in.

Part 7#

You meet a married man from Britain who is \({{ params.husband_height1 }}\) inches. What would you predict his wife’s height to be?

Answer Section#

Please enter a numeric value in.

Part 8#

How reliable is this prediction?

Answer Section#

  • The prediction based on this regression model is very reliable from the given R value.

  • Since \(R^2\) is low, the prediction based on this regression model is not very reliable.

Part 9#

You meet another married man from Britain who is \({{ params.husband_height2}}\) inches. Would it be wise to use the same linear model to predict his wife’s height?

Answer Section#

  • Yes

  • No

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.