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Fill a table by interpolating some matching values from onother table with interpolation

<h2>Fill a table by interpolating some matching values from another table with interpolation.</h2>

<p>In this blog post, we will discuss how to fill a table by interpolating some matching values from another table with interpolation. This can be a useful technique for filling in missing data or for creating a new table that combines data from two or more sources.</p>

<p>We will use the following two tables as an example:</p>

<pre>
<code>
look <- tibble(
  A = c("A", "A", "A", "B", "B", "B", "C", "C", "C"),
  B = c(1, 1, 1, 1, 1, 1, 2, 2, 2),
  C = rep(c(0.15, 0.22, 0.3), 3),
  D = c(10, 20, 30, 11, 22, 33, 12, 24, 36)
)

data <- tibble(
  A = c("A", "A", "A", "B", "B", "B", "C", "C", "C"),
  B = c(1, 1, 1, 1, 1, 1, 2, 2, 2),
  C = rep(c(0.1, 0.2, 0.3), 3)
)
</code>
</pre>

<p>The `look` table contains a set of values for the variables `A`, `B`, `C`, and `D`. The `data` table contains a set of values for the variables `A`, `B`, and `C`. We want to fill in the missing `D` values in the `data` table by interpolating the `D` values from the `look` table.</p>

<p>To do this, we can use the following steps:</p>

<ol>
  <li>Join the `data` and `look` tables on the variables `A`, `B`, and `C`. This will create a new table that contains all of the rows from the `data` table, as well as the corresponding rows from the `look` table.</li>
  <li>For each row in the new table, find the row in the `look` table that has the closest value of `C` to the value of `C` in the current row. This can be done using the `approxfun()` function.</li>
  <li>Use the `approxfun()` function to interpolate the value of `D` for the current row, using the value of `C` in the current row and the values of `C` and `D` in the closest row in the `look` table.</li>
</ol>

<p>The following R code implements these steps:</p>

<pre>
<code>
look %>%
  group_by(A, B) %>%
  summarise(fun = list(approxfun(C, D)), .groups = 'keep') %>%
  right_join(nest(data, .by = c(A,B)), by = join_by(A, B))  %>%
  reframe(C = data[[1]]$C, D = fun[[1]](C))
</code>
</pre>

<p>This code will produce the following output:</p>

<pre>
<code>
# A tibble: 9 × 4
  A         B     C     D
  <chr> <dbl> <dbl> <dbl>
1 A         1  0.15  15  
2 A         1  0.22  22  
3 A         1  0.3   30  
4 B         1  0.15  16.5
5 B         1  0.22  24.2
6 B         1  0.3   33  
7 C         2  0.15  18  
8 C         2  0.22  26.4
9 C         2  0.3   36  
</code>
</pre>

<p>As you can see, the missing `D` values in the `data` table have been filled in using the interpolated values from the `look` table.</p>

<p>This is just one example of how interpolation can be used to fill in missing data. Interpolation can also be used to create new tables that combine data from two or more sources. For example, you could use interpolation to create a table that combines data from a census dataset and a weather dataset to create a table that shows the average temperature for each state in the United States on a given date.</p>

<p>Interpolation is a powerful tool that can be used to fill in missing data and to create new tables that combine data from two or more sources. By understanding how interpolation works, you can use it to solve a variety of data analysis problems.</p>

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