Learning Check 10.1

# A tibble: 2 x 7
  term      estimate std_error statistic p_value lower_ci upper_ci
  <chr>        <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
1 intercept    4.46      0.127     35.2    0        4.21     4.71 
2 age         -0.006     0.003     -2.31   0.021   -0.011   -0.001
# A tibble: 463 x 5
      ID score   age score_hat residual
   <int> <dbl> <int>     <dbl>    <dbl>
 1     1   4.7    36      4.25    0.452
 2     2   4.1    36      4.25   -0.148
 3     3   3.9    36      4.25   -0.348
 4     4   4.8    36      4.25    0.552
 5     5   4.6    59      4.11    0.488
 6     6   4.3    59      4.11    0.188
 7     7   2.8    59      4.11   -1.31 
 8     8   4.1    51      4.16   -0.059
 9     9   3.4    51      4.16   -0.759
10    10   4.5    40      4.22    0.276
# ... with 453 more rows

Learning Check 10.2

# A tibble: 1 x 1
   stat
  <dbl>
1 0.187

1.


Call:
lm(formula = displ ~ hwy, data = .)

Coefficients:
(Intercept)          hwy  
      7.368       -0.166  
# A tibble: 2 x 7
  term      estimate std_error statistic p_value lower_ci upper_ci
  <chr>        <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
1 intercept    7.37      0.221      33.3       0    6.93     7.80 
2 hwy         -0.166     0.009     -18.2       0   -0.184   -0.148
# A tibble: 234 x 5
      ID displ   hwy displ_hat residual
   <int> <dbl> <int>     <dbl>    <dbl>
 1     1   1.8    29      2.55   -0.748
 2     2   1.8    29      2.55   -0.748
 3     3   2      31      2.22   -0.215
 4     4   2      30      2.38   -0.382
 5     5   2.8    26      3.05   -0.246
 6     6   2.8    26      3.05   -0.246
 7     7   3.1    27      2.88    0.22 
 8     8   1.8    26      3.05   -1.25 
 9     9   1.8    25      3.21   -1.41 
10    10   2      28      2.71   -0.714
# ... with 224 more rows
1.

The two are related because displacement has a direct correlation to how high or low the mpg is.

2.

Yes, because the standard error is very low.

2.

# A tibble: 23 x 2
     hwy     n
   <int> <int>
 1    12     5
 2    14     2
 3    15     1
 4    16     2
 5    17    10
 6    18    10
 7    19    10
 8    20     6
 9    22     3
10    23     5
# ... with 13 more rows
# A tibble: 19 x 2
     hwy     n
   <int> <int>
 1    15     9
 2    16     5
 3    17    21
 4    19     3
 5    20     5
 6    21     2
 7    22     4
 8    23     2
 9    24     6
10    25     6
11    26    26
12    27     6
13    29    12
14    30     1
15    32     3
16    33     2
17    35     1
18    41     1
19    44     2

We know it is different because of the changing variables through the different intergers.

3.

# A tibble: 4 x 2
    cyl     n
  <int> <dbl>
1     4  28.8
2     5  28.8
3     6  22.8
4     8  17.6

Highway fuel mileage is higher with 4-cylinder vehicles but the same as 5 cylinder vehicles.