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Consider a case in which we want to examine the effect of house value on homeupkeep expenditure using linear regression model, where dependent variable y is the upkeepexpense and independent variable x is home value. Suppose that units of y and x are both in US dollar. Let $b_{1}$ be the slope estimate and $t_{1}$ be the t-statistic value in testing $H_{0}: β_{1}= 0$.Now we convert both y and x into Canadian dollar. Let $b_{1}^{*}$ be the new slope estimate and $t_{1}^{*}$ be the t statistic value. Show that $t_{1}^{*}$ = $t_{1}$

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  • $\begingroup$ Please add the self-study tag and read its wiki $\endgroup$ – kjetil b halvorsen Feb 20 at 18:25
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    $\begingroup$ Observe that $ax/ay = x/y$, and think about how that might apply to the formula for calculating the t-statistic. $\endgroup$ – jbowman Feb 20 at 18:27
  • $\begingroup$ I'm more confused about the effect of the change in units on the standard error of $\beta_{1}$ $\endgroup$ – Nicholas Heinrich Feb 20 at 18:30
  • $\begingroup$ The standard error is in the same units as the underlying values. $\endgroup$ – whuber Feb 20 at 18:32
  • $\begingroup$ So if $a$ was the scalar representing the change to canadian dollars, it would be $t_{1}^{*}$ = $\frac{b_{1}^{*}}{se(b_{1}^{*})}$ = $\frac{ab_{1}}{ase(b_{1})}$ = $\frac{b_{1}}{se(b_{1})}$ = $t_{1}$ ??? $\endgroup$ – Nicholas Heinrich Feb 20 at 18:38

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