Math 2311 Written Homework 6 (Sections )

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1 Math 2311 Written Homework 6 (Sections ) Name: PeopleSoft ID: Instructions: Homework will NOT be accepted through or in person. Homework must be submitted through CourseWare BEFORE the deadline. Print out this file and complete the problems. Print out this file use or software and complete the problems. Write in black ink or dark pencil or type your solutions in the space provided. You must show all work for full credit. Submit this assignment at under "Assignments" and choose hw6. Total possible points: Section 5.4, Problem 2 Residual = 265 ( *69) = Section 5.4, Problem 4 Since there appears to be no pattern on this residual plot, the relationship appears to be linear.

2 3. Section 5.5, Problem 2 Scatterplot: Residual plot: plot(year,resid(lm(spending~ye ar))) b) It looks like y = e x transform y to log(y) > logspend=log(spending) > plot(year,logspend) > lm(logspend~year) Call: lm(formula = logspend ~ year) Coefficients: (Intercept) year Equation: log(y-hat) = x

3 4. Section 5.5, Problem 4

4 5. In R Studio use the data cars to determine the following. Hint: The data set is already in R studio use the quick reference guide to determine the following. Description: The data gives the speed of cars and the distances taken to stop. Note that the data were recorded in the 1920s. Format A data frame with 50 observations on 2 variables. speed numeric Speed (mph) dist numeric Stopping distance (ft) a. Give a scatter plot of the data. Determine the form, direction and strength of the relationship between speed and stopping distance (dist). b. Determine the LSRL for predicting stopping distance based on speed of the car. c. Interpret the slope of this LSRL equation. d. Determine the correlation. Give an interpretation of the correlation. e. Determine the coefficient of determination, R 2. Give an interpretation of R 2. f. One of the cars was going 25 mph and had a stopping distance of 85 feet. Determine the residual of this car. a. Postive, linear, somewhat strong relationship. b. The following is from R-studio > summary(lm(dist~speed)) Call: lm(formula = dist ~ speed) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) * speed e-12 *** --- Signif. codes: 0 *** ** 0.01 * Residual standard error: on 48 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 48 DF, p-value: 1.49e-12

5 LSRL: yy = xx c. Interpret of the slope ββ 1 = , for each additional mph of speed, the stopping distance is estimated to increase by about 4 ft. d. From R: > cor(speed,dist) [1] This is a strong positive relationship between speed and stopping distance. e. R 2 = , About 65% of the variation in the stopping distance can be explained by this least squares equation. f. For 25 mph, the predicted y = (25) = ft. Residual = observed y predicted y = = Section 5.6, Problem 4 The following two-way table describes the age and marital status of American women in The table entries are in thousands of women. Age Single Married Widowed Divorced Total ,008 3, , ,658 21, ,224 31, ,975 24,462 2,570 4,755 33, ,255 8, ,544 Total 18,541 56,838 11,290 9,161 95,830 a) The Marginal distributions are the totals for the rows and columns: For Age Age Total For Marital Status: Single 18, , , , ,544 Married 56,838 Widowed 11,290 Divorced 9,161

6 b) c) 71.35% d) 10.1% e) Here are the conditional distributions for married and Single Married Widowed Divorced Notice that there are higher percentage of single in age group, where the percentage of Widowed is much smaller (essentially zero).

7 For problems 7 10 circle the best answer. 7. In the least-squares regression line, the desired sum of the errors (residuals) should be a. positive b. negative c. zero d. maximized 8. Suppose that a least squares regression line equation is ˆy = x and the actual y value corresponding to x = 10 is 19, what is the residual value corresponding to y = 19? a b c d A prediction of the world s population in the year 2088 is an example of. a. An outlier b. Seasonality c. Extrapolation d. Correlation 10. An observation that causes the values of the slope and the intercept in the line of best fit to be considerably different from what they would be if the observation were removed from the data set is said to be a. A causation variable b. Extrapolation c. Influential d. A residual