R Problems for PS 8 -- 

11.4

a) 

> bookvalues <- c(10,12,9,27,47,112,36,241,59,167)
> auditvalues <- c(9,14,7,29,45,109,40,238,60,170)
> prob4 <- lm(auditvalues ~ bookvalues)
> summary(prob4)

Call:
lm(formula = auditvalues ~ bookvalues)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.7557 -2.1477 -0.4228  1.4803  3.7178 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.7198     1.1764   0.612    0.558    
bookvalues    0.9914     0.0114  86.994  3.4e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 2.666 on 8 degrees of freedom
Multiple R-squared: 0.9989,     Adjusted R-squared: 0.9988 
F-statistic:  7568 on 1 and 8 DF,  p-value: 3.401e-13 

The estimated change in audited value for a $1 increase
in book values is just the slope of the least squares
regression line -- .9914

b)  The estimate for the audited value corresponding
to a book value of 100 is .7198 + (.9914)(100) = 99.86.

11.9

a - c:

cylvol <- c(1.8,1.5,2.0,2.5,1.8,2.5,1.6,1.5)
horses <- c(51,51,115,150,126,150,118,106)

Call:
lm(formula = horses ~ cylvol)

Residuals:
    Min      1Q  Median      3Q     Max 
-50.858  -7.746   2.522  23.806  29.177 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   -15.45      54.84  -0.282   0.7876  
cylvol         65.17      28.30   2.303   0.0609 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 30.48 on 6 degrees of freedom
Multiple R-squared: 0.4692,     Adjusted R-squared: 0.3807 
F-statistic: 5.303 on 1 and 6 DF,  p-value: 0.06087 


> plot(cylvol,horses)
> abline(lm(horses~cylvol))

d)  The estimate would be -24.01 + (69.22)(1.9) = 107.508

1.14

> time <- c(.1,.15,.2,.25,.3,.35,.4,.45,.5,.55)
> surv <- c(1,.95,.95,.90,.85,.7,.65,.60,.55,.40)

> prob14 <- lm(surv~time)
> summary(prob14)




Call:
lm(formula = surv ~ time)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.059091 -0.031894  0.001515  0.029242  0.062121 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.18242    0.03445   34.32 5.68e-10 ***
time        -1.31515    0.09697  -13.56 8.39e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.04404 on 8 degrees of freedom
Multiple R-squared: 0.9583,     Adjusted R-squared: 0.9531 
F-statistic: 183.9 on 1 and 8 DF,  p-value: 8.393e-07 


> plot(time,surv)
> abline(lm(surv~time))

69.  

a)

> year <- c(-7,-5,-3,-1,1,3,5,7)
> sales <- c(18.5,22.6,27.2,31.2,33.0,44.9,49.4,35.0)

> a69 <- lm(sales ~ year)
> summary(a69)

Call:
lm(formula = sales ~ year)

Residuals:
     Min       1Q   Median       3Q      Max 
-10.4083  -1.5381  -0.5774   1.9000   7.6155 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  32.7250     2.1297  15.366  4.8e-06 ***
year          1.8119     0.4647   3.899    0.008 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 6.024 on 6 degrees of freedom
Multiple R-squared: 0.717,      Adjusted R-squared: 0.6698 

b)

> b69 <- lm(sales ~ year + I(year^2))
> summary(b69)

Call:
lm(formula = sales ~ year + I(year^2))

Residuals:
     1      2      3      4      5      6      7      8 
 2.242 -0.525 -1.711 -2.415 -4.239  5.118  8.156 -6.625 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  35.5625     3.1224  11.390 9.13e-05 ***
year          1.8119     0.4481   4.044  0.00988 ** 
I(year^2)    -0.1351     0.1120  -1.206  0.28167    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 5.808 on 5 degrees of freedom
Multiple R-squared: 0.7808,     Adjusted R-squared: 0.6931 
F-statistic: 8.904 on 2 and 5 DF,  p-value: 0.0225 

F-statistic:  15.2 on 1 and 6 DF,  p-value: 0.007996