# Final

**Created:**2012-04-14

**Last Modified:**2012-04-15

*y*predicted by

*x*, we assume repeated responses of

*y*are ________ of each other.

Independent

(It is an expected condition that the individuals in the study are unaffected by one another.)

A real estate firm collected data from home sales to study the relationship between area of living space measured in square feet (

*x*) and the selling price in dollars (

*y*). The 95% confidence interval for the population slope

*β*is 62.37 ± 7.18. From this result, we are 95% confident that the least-squares estimate for slope is between about 54.19 and 68.55.

**→**The interval estimate is saying something about the true value of slope for the population regression line. Specifically, what can be said is that we are 95% confident that the selling price increases by between about $54.19 and $68.55 for each additional square foot of living space.

*y*will vary when

*x*is held fixed at different values. All of the curves have the same

*σ*, so the variability of

*y*is the same for all values of

*x*.

*change*

What formula is this:

*ŷ* = *a* + *bx*

What do the symbols mean in the following equation:

*ŷ* = *a* + *bx*

a = y intercept

b = slope

x = x variable used to predict y

*y*about the population regression line.

residual = observed y - predicted y

(or = *y* − *ŷ *)

1) Linearity (straight line)

2) Normality

3) Independence (no matched pairs, blocking, etc)

4) Equal standard deviations (no funnels)

That there is no linear relationship between x and y in the population.

or

The mean of y does not change at all when x changes.

So, *H*_{0}: *β* = 0 means there is no relationship.

*np*(sample x proportion) is larger than 10.

Historically, returns on investments in the stock market are about 7% per year. The 7% figure is a:

Population p

sample p

not a p

^{2}/expected

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