Now make the prediction for next year January or x=13 ...

   
    val p1=coeff_df.withColumn("pred13", col("w0")+ lit(13)*col("w1") )

    val pred_df=sale_df.join( p1, Seq("shop","product"), "leftouter").drop("w0").drop("w1").
                        withColumn("next_jan",udfRound( p1("pred13") ) ).drop("pred13")

Result:

pred_df.orderBy("shop","product").show()

+----------+-------+----+----+----+----+----+----+----+----+----+----+----+----+--------+
|      shop|product| jan| feb| mar| apr| may| jun| jul| aug| sep| oct| nov| dec|next_jan|
+----------+-------+----+----+----+----+----+----+----+----+----+----+----+----+--------+
|  megamart|  bread| 371| 432| 425| 524| 468| 414|null| 487| 493| 517| 473| 470|508.3085|
|  megamart| cheese|  51|  56|  63|null|  66|  66|  50|  56|  58|null|  48|  50| 51.9646|
|  megamart|   milk|null|  29|  26|  30|  26|  29|  29|  25|  27|null|  28|  30| 28.1958|
|  megamart|   nuts|1342|1264|1317|1425|1326|1187|1478|1367|1274|1380|1584|1156|1362.894|
|  megamart| razors| 599|null| 500| 423| 574| 403| 609| 520| 495| 577| 491| 524|516.0467|
|  megamart|   soap|null|   7|   8|   9|   9|   8|   9|   9|   9|   6|   6|   8|     7.4|
|superstore|  bread| 341| 398| 427| 344| 472| 370| 354| 406|null| 407| 465| 402|428.2097|
|superstore| cheese|  57|  52|null|  54|  62|null|  56|  66|  46|  63|  55|  53| 56.4189|
|superstore|   milk|  33|null|null|  33|  30|  36|  35|  34|  38|  32|  35|  29| 33.3631|
|superstore|   nuts|1338|1369|1157|1305|1532|1231|1466|1148|1298|1059|1216|1231|1183.894|
|superstore| razors| 360| 362| 366| 352| 365| 361| 361| 353| 317| 335| 290| 406|339.3788|
|superstore|   soap|   8|   8|   7|   8|   6|null|   7|   7|   7|   8|   6|null|     6.5|
+----------+-------+----+----+----+----+----+----+----+----+----+----+----+----+--------+