Final - Statistics 121 with Christensen at Brigham Young University

Daniel C.

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In a linear regression of 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.)

True or False:
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.

False

→ 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.

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The Normal curves show how 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.

A slope is a rate of ______.

change

What formula is this:

ŷ = a + bx

Least-squares regression line

What do the symbols mean in the following equation:

ŷ = a + bx

a = y intercept

b = slope

x = x variable used to predict y

The standard deviation σ, which describes the __________ of the response y about the population regression line.

variability

How do you find a residual?

residual = observed y - predicted y

(or = y − ŷ )

______ are the degrees of freedom for regression.

n-2

Conditions for inference

1) Linearity (straight line)

2) Normality

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

4) Equal standard deviations (no funnels)

A regression line with a slope 0 suggests?

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

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

So, H₀: β = 0 means there is no relationship.

How do check normality for p?

Check that the np (sample x proportion) is larger than 10.

What is a safe value for p*?

0.5

How do you find p-hat?

number of successes in the sample/n

You must find _______ before random sampling.

the sample size

greater than

less than

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

not a proportion

The chi-squared statistic is _________ across each cell in the table?

(observed - expected) ²/expected

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