Exam 8: Regression, Associations, and Predictive Modeling

What is the probability that she does not sell a garment until the 7th customer? Show work.

Describe an advantage of the placebo.

It is possible that the distance that a city is from the ocean could affect its average January low temperature. Coast gives an approximate distance of each city from the East Coast or West Coast (whichever is nearer). Including it in the regression yields the following regression table: Dependent variable is:JanTemp R squared $= 87.6 \% \quad$ R squared (adjusted) $= 86.9 \%$ $\mathrm { s } = 4.878$ with $55 - 4 = 51$ degrees of freedom \begin{array} { l c c c c } \text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } 8611.86 & 3 & 2870.62 & 121 \\ \text { Residual } & 1213.67 & 51 & 23.7974 & \end{array}\\ Variable Coefficient SE(Coeff) t-ratio P-value Intercept 111.878 6.167 18.1 \leq0.0001 Lat -2.47722 0.1307 -19.0 \leq0.0001 Long 0.221997 0.0462 4.81 \leq0.0001 Coast -0.674929 0.0901 -7.49 \leq0.0001 And here is a scatterplot of the residuals: $\text { Write a report on this regression. Interpret the coefficients and } R ^ { 2 } \text {. Are the conditions met? }$

Name the sampling strategy in each plan.

Annual review You are up for your annual job performance review. You estimate there's a 30% chance you'll get a promotion, a 40% chance of a raise, and a 20% chance of getting both a raise and a promotion. a. Find the probability that you get a raise or promotion. b. Are the raise and the promotion independent events? Explain.

Is the $25 warranty a wise purchase for you? Given that you will probably buy dozens of devices over the next decade, are these types of warranties a wise purchase for you?

What is the probability that a randomly selected bicycle will have a kickstand or a water bottle Holder?

As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Comment on their statements.

Which of the explanatory variables appear to be associated with the number of skiers, and which do not? Explain how you reached your conclusion.

Does the value of s concern you? How might you deal with this data differently to address this problem?

They actually select a random sample of 525 employment records, and find that 229 of the people are females. Create the confidence interval.

The two samples whose statistics are given in the table thought to come from populations with Equal variances. What is the pooled estimate of the population standard deviation? n Mean SD 50 22 3 55 25 4

Does donating blood lower cholesterol levels? 50 volunteers have a cholesterol test, then donate Blood, and then have another cholesterol test. Which aspect of experimental design is present?

Could eye color be a warning signal for hearing loss in patients suffering from meningitis? British researcher Helen Cullington recorded the eye color of 130 deaf patients, and noted whether the patient's deafness had developed following treatment for meningitis. Her data are summarized in the table below. Test an appropriate hypothesis and state your conclusion.

Which service contract should the company expect to cost more each year? How much more? With what standard deviation?

A researcher identified 100 men over forty who were not exercising and another 100 men over forty With similar medical histories who were exercising regularly. She followed all the men for several Years to see if there was any difference between the two groups in the rate of heart attacks. This is a …

Taxi tires A taxi company monitoring the safety of its cabs kept track of the number of miles tires had been driven (in thousands) and the depth of the tread remaining (in mm). Their data are displayed in the scatterplot. They found the equation of the least squares regression line to be tread $= 36 - 0.6$ miles, with $r ^ { 2 } = 0.74$ . a. Draw the line of best fit on the graph. (Show your method clearly.) b. What is the explanatory variable? c. The correlation $r =$ d. Describe the association in context. e. Explain (in context) what the slope of the line means. f. Explain (in context) what the $y$ -intercept of the line means. g. Explain (in context) what $R ^ { 2 }$ means. h. In this context, what does a negative residual mean?

All 423 Wisconsin public schools were all given a rating by the Wisconsin Department of Public Instruction based on several variables. The mean rating reported was 71.5 and the standard deviation was 4.87. To do a follow-up study a random sample of 40 schools was selected. In this sample, the mean rating was 70.9. One of the researchers is alarmed, thinking the report may have been mistaken. Do you think this sample result is unusually low? Explain.

A factory has 20 assembly lines producing a popular toy. To inspect a representative sample of 100 Toys, quality control staff randomly selected 5 toys from each line's output. Was this a simple Random sample?

The SPCA collects the following data about the dogs they house. Which is categorical?