Policy inquiry and analysis using quantitative regression methods

¶ … Flowers bloom mainly according to temperature and length of daylight, with a minimal amount of moisture required.

b) This might be causal. Longer daylight hours increase heat, and help cause flowers to bloom, but not entirely. For example, the Arctic gets 24 hours of daylight at times, but it is too cold for most flowers to bloom. Flowers are the main source of pollen, whether from grass, trees, or "decorative" flowers.

c) Prices and sales volumes are causal, to a degree. It does not matter how cheap something is if nobody wants it. Conversely, if it is super-expensive, someone may be rich enough buy it.

d) This is not causal. The increase in height is due primarily to age, which then is the proximate cause of reading ability, due to experience gained as one ages.

2)

a) In 1999, the average Asian made about twice as much as the average black in the United States.

b) The average Hispanic person earned $2,825 more than the average black person in the United States did in 1999, per year.

c) Whites ranked second in terms of median income by race/origin in the United States in 1999.

d) The percentage difference for Asians' median income in 1999 was 20% more than any other group.

3)

Homicide Rate in Texas

Year

Homicides per 100,000 people

Absolute Differences

Relative Differences

Percentage Change

Percentage Change using the average

1990

16 = x, V1

y -- x

10 -- 16 =

|-6| = 6

y/x = 10/16 = 0.625

[(V2-V1) / V1] x 100 =

[(10-16)/16] x 100 =

-37.5%

((V2 - V1) / (V2 + V1)/2) x 100 = [(10 -16)/((10+16)/2)] x 100= -46%

1995

10 = y, V2

a) From 1990 to 1995, the homicide rate in Texas dropped from 16 per 100,000 people to 10 per 100,000 people, 6 people less.

b) In 1995, the homicide rate per 100,000 people in Texas was 0.625 what it was in 1990 (column 3).

c) Between 1990 and 1995, the homicide rate in Texas dropped 37.5%, decreasing from 16 per 100,000 people to 10 per 100,000 people.

d) In 1995, the homicide rate in Texas was only 46% of its 1990 rate, decreasing from 16 per 100,000 people in 1990 to 10 per 100,000 people in 1995.

4) the 95% CI = ?k ± (1.96 x s.e. k), where 1.96 is the critical value for p < 0.05 with a two-tailed test

Lower ?k - (1.96 x s.e. k)

Upper ?k + (1.96 x s.e. k)

a) 90% CI for 1998 median income for all households

a. Upper: 39744 + (1.64)(387) = 40378

b. Lower: 39744 - (1.64)(387) = 39109

b) Change in Real Household Income between 1998 and 1999 statistically significant at p

a. For all households? No. They overlap.

i. 1998

1. Upper: 39744 + (1.64)(387) = 40378

2. Lower: 39744 - (1.64)(387) = 39109

ii. 1999

1. Upper: 40816 + (1.64)(314) = 41331

2. Lower: 40816 - (1.64)(314) = 40301

b. For family households? No. They overlap.

i. 1998

1. Upper: 48517 + (1.64)(419) = 49204

2. Lower: 48517 - (1.64)(419) = 47830

ii. 1999

1. Upper: 49940 + (1.64)(449) = 50676

2. Lower: 49940 - (1.64)(449) = 49204

c. For non-family households? No. They overlap.

i. 1998

1. Upper: 39744 + (1.64)(387) = 24741

2. Lower: 39744 - (1.64)(387) = 23177

ii. 1999

1. Upper: 40816 + (1.64)(314) = 25294

2. Lower: 40816 - (1.64)(314) = 23838

c) No statistically significant differences.

type of household

1998

Upper

Lower

1999

Upper

Lower

Overlap:

median income

90% CI +/-

median income

90% CI +/-

i. The t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error. In this case, the estimated coefficient of error is 0.262, and the standard error is 0.038, so the t-statistic is 6.89.

ii. Since the sample size is so large (450), the confidence interval of 95% is 1.96

iii. For the female coefficient of error of 0.262, because the t-statistic is so large, ** could be used, because ? For t-distributions is 2.576 at the 99% interval, well below 6.89.

b)

i. unknown

ii. unknown iii. unknown

iv. Estimates of coefficients from within a regression model are generally not independent of one another, so cov (?j, k,)?0. In such cases, information on the covariance between ?j and ?k must be taken into account when calculating the standard error of the difference or confidence intervals. Covariance is not given, so no estimation of statistical significance can be made.

c)

i. One model deals with verbal SAT scores, another deals with ethnicity, and another deals with gender. They are laid out by model.

ii. Unknown.

iii. Estimates of coefficients from within a regression model are generally not independent of one another, so cov (?j, k,)?0. In such cases, information on the covariance between ?j and ?k must be taken into account when calculating the standard error of the difference or confidence intervals. Covariance is not given, so no formal estimation of statistical significance can be made.

6)

a) Null hypothesis: a longer season is unrelated to the size of the bird population. Hypothesis: a longer season is related to the size of the bird population.

b) We now know the values for "slope" and "Y-intercept." We can use the number of days in the season to find the number of birds surviving the season. Approximately 547,000 birds exist, and 214 are killed every day during hunting season, with a standard of error of 415 birds either way. I would assume that there have 35 past hunting seasons. Approximately 15% percent of the variation in the number of birds can be explained by the length of the hunting season.

7)

Sy/x is a function of Sy, but we're not given Sy. Instead, we're given Sb. The smaller Sb is in relation to Sy/x, the more precise the relationship is, though we have no measure of the strength of the correlation. However, a larger r2 indicates a good positive line. So, for every 50 cent increase in the price of gas, there will be approximately 93 more riders, more or less ~17.