Chapter 12
Musa is interested in the relationship between hours spent studying and caffeine consumption among students at his school. He randomly selects 20 students at his school and records their caffeine intake (mg) and the amount of time spent studying in a given week. Here is computer output from a least-squares regression analysis on his sample: Predictor Coef SE Coef T P Constant 2.544 0.134 18.955 0.000 Caffiene 0.164 0.057 2.862 0.010 S = 1.532 R squared = 60% Which of these is a 95\%percent confidence interval for the slope of the least-squares regression line?
0.164 +- 2.101*0.057 t half alpha = 0.057
Kadence took a random sample of 24 students at her school and asked them how much they typically slept on a school night versus a weekend night. Here is computer output from a least-squares regression analysis on her sample: Predictor Coef SE Coef Constant 3.182 2.319 School night 0.789 0.237 S = 1.75 R squared = 20.9% Which of these is an appropriate test statistic for testing the null hypothesis that the population slope in this setting is 000?
0.789/0.237 t = bi-bio/Se(bi) = 0.789/0.237
A regression analysis yields the following information: ^Y=2.21+1.49X, n=10 , ^σ=1.66, ∑Xi=32, ∑(Xi−¯X)^2=31.6 Compute the 95% prediction interval when X = 4. Compute the 95% confidence interval for x = 4
4.118, 12.226 6.8426, 9.4974 for both: y^ = 8.17 thalf alpha = 2.306 Sxx = 31.6 Prediction: 8.17 +- 4.052 Confidence: 8.17 +- 1.3274
The regression equation is ^Y=29.29−0.96X , the sample size is 8, and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope? What is the critical value to test the significance of the slope at the 0.01 significance level?
4.363 t is bi-bio/s(bi) = -0.96-0/0.22 = 4.363 +-3.707 thalf alpha = t0.01/2 = t0.005,6 = +-3.707
A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: ANOVA Regression Residual Total df 1.00 8.00 9.00 SS 13555.42 693.48 14248.90 MS 13555.42 86.68 F 156.38 Significance F 0.00 What is the value of σ^? what is coefficient of determination
9.95 SSE = (n-2)sigmasquared 693.48 = 9-2 sigma squared 0.9513 SSR/SST = Rsquared 13555.42/14248.90
Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal.
all of them
When comparing the 95% confidence and prediction intervals for a given regression analysis ______________.
confidence interval is narrower than prediction intervals
In regression analysis, error is defined as Ybar −Y: true or false
false
Sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?
number of contacts
The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y: true or false
true
The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information. City Police Crimes Oxford 23 18 Straksville 24 15 Danville 30 9 Athens 33 11 Holgate 24 9 Carey 20 22 Whistler 19 24 Woodville 27 10 What is the estimated y-intercept and the slope of the regression line?
y - intercept: 39.9 Slope: (-)1.00625 bi= sum of xy - nmeanxmeany/sum xisquared - nxbarsquared sumxy = 2789 mean x = 25 mean y = 14.75 sum xi squared = 5160 x bar squared = 625 bo = ybar - bi xbar